Inside the occupied government building, teenagers strolled through the regional council chamber and took selfies in the speaker's chair, now flanked by the flags of Russia and the Soviet-era independent republic of Donetsk.

Riot policemen with shields and helmets lined the corridors, but they seemed in no particular hurry to remove the pro-Russian activists who had burst into the 11-storey building a day before and appointed their own "people's governor".

"We will not leave until our demands are met," said Olexsander, aged 42, a self-appointed commander in the "local resistance" camped out in the council chamber. "Donetsk belongs with Russia," he said.

Pro-Russian groups have called on local deputies to declare the government in Kiev illegitimate, to put all security forces under regional control and to withhold taxes from the capital. They also want a referendum on the region's future status – although they have yet to agree on the question to be asked, and the new government in Kiev has said that any such vote would be illegal.

But while the Russian tricolour still fluttered over the parliament building on Tuesday night, hundreds of protesters gathered in the square outside, waving the blue and yellow flag of Ukraine, and calling for the country to come together in unity.

In the wake of Russia's armed intervention in Crimea, tensions are simmering across the Russian-speaking provinces of eastern Ukraine.

Reports that Russian military vehicles had gathered on Ukraine's border near Kharkiv, Donetsk and Luhansk have triggered rumours that the Kremlin is preparing to pull another intervention in Ukraine's eastern regions.

Kiev says Moscow has organised the demonstrations and sent hundreds of Russian citizens across the frontier to stage protests which would provide the pretext for a military advance – a charge which was vehemently denied by protestors in the Donetsk parliament.

"I can tell you from my heart this is absolutely not true. The people here are only locals," said Olexsander.

Large pro-Russian demonstrations have been held in Odessa, Kharkiv and Donetsk, and Russian flags raised atop administrative buildings. The Kharkiv protests descended into violence when counter-demonstrators calling for Ukrainian unity were badly beaten by Russian nationalists.

The deep divisions in Donetsk – the home town of ousted president Viktor Yanukovych – were acted out over the course of the day in a series of rival protests for and against Ukrainian unity.

Many locals feel marginalised by the new administration in Kiev, which they describe as the fruit of a power grab by pro-Western "bandits".

In the morning, several hundred people gathered outside the occupied parliament, calling for eastern Ukraine to join Russia. Addressing the crowd over a loudspeaker, one woman asked why the pro-European demonstrators had been consecrated as heroes, while the Berkut riot police unit – blamed for the deaths of dozens of protesters – has been disbanded.

"Why are our boys not heroes? They suffered in Kiev. They were beaten and humiliated, made to go on their knees. Now they are all forgotten. They were just fired from their jobs. If they had not protected us, then those mad protesters would have burnt the whole of Kiev," she said.

Tensions ran high when a pro-Europe group mounted a counter-demonstration. "We are not trying to separate the country," said one man angrily. "The protesters in Kiev pretended to stand for peace and freedom, but they are hijacking the whole country".

But later on a string of "pro-unity" demonstrations across the city attracted people from many walks of life.

Waving a Ukrainian flag alongside several other local clergy, Maxim Gorinov, 37, a pastor at a local evangelical church, said he wanted Donetsk to stay in Ukraine.

"I am Russian, my family speaks Russian, but I am against separatism. We don't want Russian troops here to separate us by force," he said.

Significantly, the unity movement in Donetsk is backed by "ultras" – fanatical supporters of the local Shakhtar football club, one of Ukraine's two top teams. In the violent street protests which eventually forced Yanukovych to flee the country, Shakhtar ultras fought alongside their arch-rivals from Kiev's Dynamo. On Sunday the ultras from each team played against each other in the country's capital in a continued display of unity. The game ended in an uncontroversial 1-1 draw.

On Tuesday evening the largest pro-unity rally in Donetsk attracted more than one thousand people. Protesters carried Ukrainian flags and chanted "Donbas is Ukraine" and "Putin go home". Shakhtar football club ultras flanked ordinary demonstrators saying they were there "to protect the people".

"Why should we have a referendum? It is unconstitutional for Donetsk to do this on its own", said Dimitry Goryainov, a urologist who joined the rally. "We are against the separation of Ukraine," he added. "The main problem here is people are scared the new government needs to reassure them by calling parliamentary elections after the presidential election."

Even the members of the local Cossacks – a staunchly pro-Russian group – are firmly against military intervention by Moscow.

"Ukraine can solve its internal problems on its own," said the Cossacks' leader, Vadim Zhmarin. "We are against any troops entering Ukrainian soil – Nato or Russia," he added.

Unity activists' leaders claimed a moral victory, and said an even bigger march will be held on Wednesday. Alex Ryabchyn, a PhD student in international economics, said he had never seen so many Ukrainian flags flying in Donetsk as he had now. "This really is a historical day for our city," he added.

Inside the parliament, pro-Russian demonstrators bedded down for the night.

• The headline of this article was amended on 5 March 2014 to more accurately reflect its contents.