(Repeats no change to text)
By Lina Kushch and Alessandra Prentice
DONETSK/KHARKIV, Ukraine, March 4 (Reuters) - More than 1,000 demonstrators with Ukrainian flags took to the streets of the eastern Ukrainian city of Donetsk on Tuesday, for the first time outnumbering pro-Moscow youths who have seized its government building, which flies the Russian flag.
President Vladimir Putin's declaration on Saturday that Russia had the right to invade Ukraine was accompanied by pro-Russian demonstrations across Ukraine's mainly Russian-speaking south and east.
But in the four days since, the tide of opinion in eastern cities appears to be turning back towards Kiev.
Bearing placards with slogans such as: "I am Russian. I don't need protection," the protesters marched near the occupied regional government building, staying far enough away to avoid clashing with the pro-Russian youths still inside.
"My parents are from Russia. I was born in Ukraine, but I am Russian. My children and grandchildren were born here. We are for Ukraine," said Natalia Sytnik, who turned out to protest against the prospect of a Russian invasion.
"We did not ask for help. I don't want him, Putin, to bring tanks here. I don't want them to shoot at my kids. Let him hear us: 'Do not defend me from anyone. No one is attacking me'."
The government building's lower floors were seized on Monday by followers of Pavel Gubarev, owner of a Donetsk advertising business, who has declared himself "the people's governor", demanded the region's ties with Kiev be severed and all control over regional security forces be placed in his hands.
His followers chant "come, Putin!" and wave Russian flags. On Monday they barricaded lawmakers into the building and demanded they pass a bill calling for a referendum on regional autonomy. The lawmakers passed a bill calling for a "referendum", but to the chagrin of the pro-Moscow protesters it made no mention of what question would be asked or when.
Kiev says the protests - which erupted simultaneously in Kharkiv, Odessa, Dnipropetrovsk and several other cities hours before Russia's parliament voted to grant Putin authority for armed force - were organised by Moscow as a pretext to invade. It says most of the pro-Russian demonstrators were Russians brought across the border in busloads.
It is certainly clear that many of Gubarev's followers are not from Donetsk, where locals speak Russian with an easily recognisable accent. One, who said he was a miner from a nearby village, was unable to name either the village or a single mine in a region known across the ex-Soviet Union for its coal.
Nevertheless, the pro-Moscow demonstrations have also attracted many local sympathisers in a region with longstanding grievances towards Kiev, where there was genuine alarm at the uprising that toppled native son Yanukovich.
"I support these (pro-Russian) meetings, because I want the city to resolve its difficult questions by itself, independently of the central authorities," said Olga, a law student.
"Of course the fact that here the doors (of the government building) have been torn open is not very nice, but in general the demonstrations here are less violent than in Kiev, where there are weapons and Molotov cocktails and so forth."
But there are increasing signs that the tactics used by the pro-Moscow protesters and the prospect of a full-scale armed invasion have pushed many in the east to stick with Kiev.
CHAINS AND AXE HANDLES
In Kharkiv, another eastern city, Saturday's protest turned violent, with scores of people injured when pro-Russian demonstrators armed with chains and axe handles stormed the regional parliament building and trashed it, savagely beating the heavily outnumbered civilians who turned out to defend it.
The incident seems to have backfired, however, causing a backlash and alarming the public. The demonstrators lost more credibility after a social media page was discovered showing that the young man who put a Russian flag atop the regional parliament building had described himself as a Muscovite.
Since then the city has been quiet and the Ukrainian flag is back. On Tuesday around 200 policemen in full riot gear stood four-deep along the front of the building, with a further 20 helmeted officers barricading the entrance with metal shields.
"Where were they on Saturday when we needed them?" said Lyudmila Shevchenko, a teacher standing in a small group of people wearing ribbons in yellow and blue Ukrainian colours. "We're still scared to be here, but we need to show our support for Ukraine. We don't need Europe, Russia or any talk of a split. Putin should mind his own business."
Across the street from the police blockade, a pro-Russian crowd had dwindled to about 100 people. Most wore orange and black ribbons, a sign of their loyalty to Russia, while one waved a handmade sign with the writing "Russia, help us!".
Flyers being handed round advertised a large protest against Kiev's "fascist regime" scheduled for Wednesday.
"Far-right groups from the west have been coming here to cause trouble. We don't want them or any of the nationalists in Kiev telling us what to do," 21-year-old Sasha said through a face mask. "We're here today, we'll be here tomorrow - we're not going anywhere. It could get ugly again."
OLIGARCHS ON BOARD
The authorities in Kiev have made one important bet that could prove decisive in the east: naming some of the country's richest men as governors of their home regions.
Ukraine's oligarchs, who once mainly backed Yanukovich, have lined up behind the new authorities in Kiev. Most have their own roots in the east, where Ukraine's mineral resources and factories are mainly located.
In Donetsk, the newly appointed governor is Sergei Taruta, a metals baron with tens of thousands of employees in the east.
By Tuesday he had yet to make his first appearance since being awarded the job two days before. In an interview, he said the pro-Russian demonstrations were organised by Moscow, lacked genuine broad support and would soon fizzle out.
"I am absolutely convinced that the southeast, in its majority, stands for the position of a united Ukraine. Law and order will be restored," he told the weekly Zerkalo Nedeli newspaper in Kiev. "The plotters will not succeed in achieving their desired effect."
In Dnipropetrovsk, another eastern city that has seen unrest, Kiev is counting on the clout of an even wealthier oligarch. The new governor is billionaire industrialist Ihor Kolomoyskiy, Ukraine's third richest man.
Shevchenko, the Kharkiv schoolteacher, compared Ukraine since Yanukovich was deposed to a young child who would soon grow out of its unruly behaviour.
"Of course it's weak and doesn't always make the right decisions, but it will grow and flourish in time." (Writing and additional reporting by Peter Graff in Kiev; Editing by Will Waterman)