With jaunty pop numbers about "expelling the fascist junta", rousing war poetry and – somewhat incongruously – a parade of performing dogs, the leaders of the self-proclaimed Donetsk People's Republic celebrated on Monday what they see as victory over Kiev.

Held in the shadow of an austere second world war monument in central Donetsk, the event was officially a celebration of the 71st anniversary of the liberation of the Donbass region from Nazi occupation. But the parallels with the current Ukrainian conflict, where local leaders and Russian President Vladimir Putin have compared the Ukrainian government to the Nazis, were not hard to find.

The self-proclaimed prime minister of the Donetsk People's Republic, Alexander Zakharchenko, signed a peace deal in Minsk last Friday with Ukraine's representative, former president Leonid Kuchma. The deal included a ceasefire, an "all-for-all" prisoner exchange, and increased autonomy for Donetsk and Luhansk regions, with the implicit assumption that they would remain part of Ukraine.

After the talks, however, Zakharchenko said the regions were still planning to declare full independence, suggesting the region could become a kind of "breakaway state" with Russian backing. In Donetsk, which had come under heavy shelling in recent weeks as both the rebels and the government forces fired into residential areas, the rebels see the agreement as a victory, "freezing" the conflict and forcing the Ukrainian government to negotiate with the rebel leaders, whom it had previously dismissed as "terrorists".

Since the ceasefire was signed, each side has accused the other of breaking the truce, most notably in the port city of Mariupol, where Ukrainian checkpoints have come under heavy artillery fire from the pro-Russian side.

Zakharchenko, speaking at the rally in Donetsk, said all Ukrainian forces must leave the eastern regions, "or we will throw them out". Kiev's forces lost a lot of ground in the two weeks before the ceasefire, with evidence suggesting Russia sent reinforcements of armour and soldiers over the border, something Moscow has vehemently denied. But Ukrainian troops still control Donetsk airport and many other key sites, leading to fears the fighting could resume at any moment.

Alexander Khryakov, a minister in the Donetsk government, told the Guardian that a "real ceasefire" would only happen when Kiev was fully defeated.

"Today we are celebrating the liberation of the Donbass from fascism," he said. "And that is a battle that is still going on. The ceasefire will come when there are no more fascists. And not just in the Donbass but in Kiev as well."

Ukraine's president Petro Poroshenko made a surprise visit on Monday to the southern port city of Mariupol, which has come under heavy artillery fire, after separatist fighters allegedly backed by Russian support took the town of Novoazovsk, further along the coast and near the border with Russia, a fortnight ago.

On Saturday night, a day into the ceasefire, the edge of the city came under fire and the Donetsk rebels wrote on their Twitter account that they were "taking Mariupol", although they later said they were reacting to provocations from the Ukrainian side and were keeping the ceasefire. On Sunday, Ukrainian fighters claimed the rebels had again shelled their positions on the outskirts of Mariupol, leading to casualties, and that they had began to return fire, although Monday was largely quiet.

Poroshenko, who spoke to a crowd of steel workers in Mariupol, promised that the pro-Russians would face a "crushing defeat" if they tried to take the city, which would give the Donetsk rebels an outlet to the sea.

"I have ordered (the military) to secure the defence of Mariupol with howitzers, multiple rocket launchers, tanks, anti-tank weapons and air cover," said the Ukrainian president, dressed in military-style fatigues. "Mariupol was, is and will be Ukrainian."

A number of fighters on the Ukrainian side have said in recent days that Kiev needs the ceasefire to regroup, but will resume military operations against the "occupying forces" at the first possible opportunity.

In Donetsk, there was anger and resolution among the 1,500-strong crowd who had gathered at the rally.

"We loved Ukraine until they started bombing us, now we can never go back there," said Zinaida, a 58-year-old local. "They are fascists and they have your support. We read that you have Scotland wanting to secede there. Why don't you send your tanks there and destroy them instead of sending them here? We will be part of Russia now and will never go back to those fascists."

Donetsk, a city of 1 million in peacetime, has come to resemble a ghost town in recent weeks as more than half of the population have left, and those who remain stay indoors. While the mood at the rally was unanimous, many of those who want to remain part of Ukraine have left the city. Last month, a rare pro-Ukrainian activist was captured by rebel fighters and made to stand draped in a Ukrainian flag in a central street while passers by threw insults and projectiles at her. She was later released.

Poroshenko, from Mariupol, said the rebels had agreed to release around 1,200 Ukrainian prisoners from captivity under the terms of the Minsk agreement. There was no immediate confirmation of this from the rebel side, nor any information about whether Kiev had freed the estimated 200 prisoners it had taken among rebel fighters.