* Poroshenko offers to evacuate civilians at risk
* Ukraine reports several overnight clashes with rebels
* Report of 40 rebels killed not independently confirmed
* Poroshenko appoints chief of staff (Adds new appointments, more on corridors)
By Richard Balmforth
KIEV, June 10 (Reuters) - Ukraine's new president ordered the creation of evacuation "corridors" on Tuesday to help civilians escape fighting between pro-Russian separatists and government forces in east Ukraine.
Petro Poroshenko, who is trying to win Russia's backing for a peace plan for the east, ordered his security chiefs to create evacuation routes for civilians "to stop new casualties" in the conflict zones, his press service said.
The state security service (SBU) later said it was working with other law-enforcement bodies to establish "a safety corridor" in line with Poroshenko's proposal.
"The Head of State also instructed the government to take responsibility for the transportation of people and medical services, as well as ... provide the civilian population with drinking water, food and medicines," the presidential press service said after Poroshenko met security and defence chiefs.
The president, sworn in on Saturday, is under pressure to act swiftly and give teeth to his pledges to bring peace to the industrialised east where separatist unrest, which Kiev says is fomented by Moscow, erupted in April.
Russian Foreign Minister Sergei Lavrov, meeting the Polish and German foreign ministers in St Petersburg, welcomed Poroshenko's move as "a step in the right direction".
He has frequently called for humanitarian aid for civilians trapped by fighting in east Ukraine.
Despite the start of talks with a Russian envoy and the Organization for Security and Cooperation in Europe (OSCE), and signs that Russia and Ukraine could soon end a long-running dispute over gas supplies to Kiev, fighting has continued.
The pro-Russian separatists overnight attacked Ukrainian military checkpoints and other strategic points in eastern Ukraine but they were deflected with only minor casualties on the Ukrainian side, a government forces spokesman said.
In a three-hour battle near the airport of Kramatorsk, rebels attacked the army with mortars but government forces returned fire, destroying their position and killing 40 "mercenaries", said the spokesman, Vladyslav Seleznyov.
This figure could not be independently confirmed and there was no immediate word from the side of the separatists.
In Slaviansk, just north of Kramatorsk, two Ukrainian soldiers were wounded when rebels, who control the city, attacked an army position on the perimeter using grenade-launchers.
In Luhansk, on the border with Russia, separatist fighters opened fire on the airport and nearby Ukrainian army positions.
"The attack of the (separatist) fighters was repelled by special force units. There are no losses on the Ukrainian side," said Seleznyov.
Separatist rebellions broke out in Russian-speaking regions of eastern Ukraine in April after street protests in the capital Kiev toppled a Moscow-leaning president. Scores of separatists, members of government forces and civilians have been killed.
The pro-Western Poroshenko on Saturday pledged to end the fighting while promising to address the legitimate grievances of people in the east, by for example granting them greater autonomy and guaranteeing the status of the Russian language.
Moscow has denied fomenting the unrest and allowing mercenaries from Russia to cross the long border with consignments of arms to support the rebels.
Poroshenko's proposal on Tuesday appeared to differ from his offer on Saturday to allow fighters from Russia to return safely home as long as they put down their arms.
Ukraine said on Monday it had reached a "mutual understanding" with Russia on parts of a peace plan proposed by Poroshenko, though it gave no details and Moscow made no direct comment on the issue.
In his first working day at his desk since taking office, Poroshenko made his first moves to put a team together, naming a wealthy media entrepreneur, Borys Lozhkin, as his chief of staff.
The two men have been business partners since 2007 when Poroshenko leased one of his media outlets to Lozhkin, 42, who was already a well-known entrepreneur owning a media holding, UMH, which has established magazines including Forbes-Ukraine.
He also named a new press secretary, Svyatoslav Tseholko, a presenter for Poroshenko's 5th channel television station.
Poroshenko is expected in the coming days to name a foreign minister and defence minister, both of whom will be actors in any plan embracing Russia to end the fighting and make Ukraine's borders safe. (Writing by Richard Balmforth; editing by Janet McBride)