(Adds German foreign minister, Zakharchenko)
* Putin says Russia cannot stand aside
* Rebels shell Ukrainian naval ship in first sea attack
* Moscow may be seeking land corridor for Crimea - Berlin
* Residents flee Mariupol in fear of rebel assault
* Fifteen Russian paratroops swapped for 63 Ukrainians
By Katya Golubkova and Aleksandar Vasovic
MOSCOW/MARIUPOL, Ukraine, Aug 31 (Reuters) - Russian President Vladimir Putin called on Sunday for immediate talks on the "statehood" of southern and eastern Ukraine, although his spokesman said this did not mean Moscow now endorsed rebel calls for independence for territory they have seized.
The Kremlin leader's remarks, two days after a public appearance in which he compared the Kiev government with Nazis and warned the West not to "mess with us", came as Europe and the United States prepared possible further sanctions to halt what they say is direct Russian military involvement in the war in Ukraine.
Germany aired suspicions that Moscow might be trying to create a land corridor to supply Crimea, which it annexed from Ukraine in March, while the four-month conflict moved onto the sea for the first time on Sunday. The separatists said they had fired on a Ukrainian vessel in the Azov Sea using land-based artillery, and a military spokesman in Kiev said a rescue operation was under way.
Ukrainian troops and local residents were reinforcing the port of Mariupol on Sunday, the next big city in the path of pro-Russian fighters who pushed back government forces along the Azov Sea this past week in an offensive on a new front.
Ukraine and Russia swapped soldiers who had entered each other's territory near the battlefield, where Kiev says Moscow's forces have come to the aid of pro-Russian insurgents, tipping the military balance in the rebels' favour.
Talks should be held immediately "and not just on technical issues but on the political organisation of society and statehood in southeastern Ukraine", Putin said in an interview with Channel 1 state television, his hair tousled by wind on the shore of a lake.
Moscow, for its part, he said, could not stand aside while people were being shot "almost at point blank".
Putin's use of the word "statehood" was interpreted in Western media as implying backing for the rebel demand of independence, something Moscow has so far stopped short of publicly endorsing.
However, Putin's spokesman Dmitry Peskov said there was no new endorsement from Moscow for rebel independence. Asked if "New Russia", a term pro-Moscow rebels use for their territory, should still be part of Ukraine, Peskov said: "Of course."
"Only Ukraine can reach an agreement with New Russia, taking into account the interests of New Russia, and this is the only way to reach a political settlement."
Rebels have rallied behind the term "New Russia" since Putin first used it in a public appearance in April. Putin called it a tsarist-era term for land that now forms southern and eastern Ukraine. Ukrainians consider the term deeply offensive and say it reveals Moscow's imperial designs on their territory.
Moscow has long called for Kiev to hold direct political talks with the rebels. Kiev says it is willing to have talks on more rights for the south and east, but will not talk directly to armed fighters it describes as "international terrorists" and Russian puppets that can only be reined in by Moscow.
The deputy leader of the rebel Donetsk People's Republic, Andrei Purgin, said he was due to participate in talks in the Belarus capital Minsk on Monday. Past talks by a "contact group" involving Moscow, Kiev and the rebels have covered technical issues such as access to the crash site of a Malaysian airliner shot down in July, but not political questions.
The past week has seen Ukrainian forces flee in the path of a new rebel advance, drawing concern from Ukraine's Western allies, who say armoured columns of Russian troops came to the aid of a rebellion that would otherwise have been near collapse.
European Union leaders agreed on Saturday to draw up new economic sanctions against Moscow, a move hailed by the United States, which is planning tighter sanctions of its own and wants to act jointly with Europe.
German Foreign Minister Frank-Walter Steinmeier saw a possible link between the fighting around Mariupol and the Crimean peninsula, which is under Moscow's control but has no land border with Russia.
"It doesn't appear to be ruled out that Russia is trying to make land connections to organise supplies for the population of Crimea," he was quoted by the Maerkische Allgemeine newspaper as saying in an interview. "Russian land bridges and corridors would be just as illegal and deplorable as its annexation of Crimea."
Some residents of Mariupol have taken to the streets of the port to show support for the Ukrainian government as pro-Russian forces gain ground. Many others have fled from the prospect of an all-out assault on the city of nearly 500,000 people.
"We are proud to be from this city and we are ready to defend it from the occupiers," said Alexandra, 28, a post office clerk wearing a ribbon in blue and yellow Ukrainian colours.
"We will dig trenches. We will throw petrol bombs at them, the occupiers," she said. "I believe our army and our (volunteer) battalions will protect us."
The separatists claimed another victory with what they said was the withdrawal of Ukrainian soldiers from the airport at Donetsk, the main city in the industrial southeast.
Alexander Zakharchenko, prime minister of the "Donetsk People's Republic", told reporters in the city: "They (the Ukrainians) raised a white flag, we ceased fire."
He said the rebels had yet to consolidate control over the airport: "The airport is not their territory any more but neither it is ours yet... We will slowly take it back."
The swap of soldiers overnight at the frontier was a rare gesture to ease tension, but Kiev and Moscow have given starkly opposing accounts of how their troops came to be on each other's territory. A Russian commander said an unspecified number of Russian paratroops were swapped for 63 Ukrainian soldiers. Kiev said the Russian soldiers numbered nine.
Kiev and its allies in Europe and the United States say the new rebel offensive has been backed by more than 1,000 Russian troops fighting openly to support the insurgents. The rebels themselves say thousands of Russian troops have fought on their behalf while "on leave".
Reuters journalists on the Russian side of the border have seen Russian troops showing signs of having returned from battle, with their insignia removed or rubbed out.
Despite the evidence, Moscow denies its troops are fighting in Ukraine and says a small party of soldiers crossed the border by accident. Russian Major-General Alexei Ragozin said the paratroops were handed back after "very difficult" negotiations.
The United States and EU have gradually tightened economic sanctions against Russia, first imposed after Moscow annexed Crimea following the ousting of Kiev's pro-Russian president by protesters.
So far, however, the measures have done little to deter Putin, who gave a typically defiant public appearance on Friday in which he described Russians and Ukrainians as "practically one people" and compared Kiev's attempts to recapture rebellious cities with the Nazi invasion of the Soviet Union.
Russia is a strong nuclear power, and foreigners should understand that "it's best not to mess with us", he said.
Moscow has responded to sanctions by banning the import of most Western foodstuffs and shutting down McDonalds restaurants. The moves reinforce a sense among Russians that they are isolated from a hostile world, as in Cold War days.
Agreeing the Western sanctions has been tricky, not least because the 28-member EU must take decisions by consensus and many of its countries depend on Russian energy resources.
Nevertheless, the EU has gone further than many had predicted, agreeing to impose sanctions on Russia's financial and oil industries last month after the Malaysian airliner was shot down over rebel territory, killing nearly 300 people, most of them Dutch.
EU leaders agreed on Saturday to ask the executive European Commission to draw up more sanctions measures, which could be adopted in coming days.
The White House praised the move to "show strong support for Ukraine's sovereignty and territorial integrity". But in a sign of the difficulty in achieving an EU consensus, the leader of Slovakia said sanctions had failed so far and threatened to veto any new ones that damaged his country's national interest. (Additional reporting by Richard Balmforth, Pavel Polityuk, Vladimir Soldatkin, Mark Trevelyan, Stephen Brown, Arbi Zubayrayev and Maxim Shemetov; Writing by Peter Graff and David Stamp; Editing by Mark Heinrich)