President Vladmir Putin warned Europe to keep its hands off Ukraine on Tuesday, as Brussels sent its top foreign policy envoy to Kiev to try to mediate in the 10-week stand-off between President Viktor Yanukovych and the opposition on the streets.

Russia's intervention in Brussels followed Yanukovych's biggest concession to the opposition, the sacking of his hardline prime minister and government and a promise to repeal draconian laws criminalising protest and freedom of speech.

Putin met EU leaders for the first time since November's clash between the Kremlin and Europe over the future of Ukraine triggered the crisis in Kiev. Catherine Ashton, the EU foreign policy chief, took part in the meetings with Putin in Brussels then travelled to Kiev to try to mediate between the opposing sides.

"The more intermediaries there are, the more problems there are," Putin said. "I am not sure Ukraine needs intermediaries." He pointedly noted that European leaders would complain if Russia sent envoys to mediate in the Greek crisis of the past four years.

"I can only imagine what the reaction would be if in the heat of the crisis in Greece or Cyprus, our foreign minister came to an anti-European rally and began urging people to do something. This would not be good," Putin said. "I'm sure the Ukrainian people will sort this out and Russia is not going to interfere."

The president of the European council, Herman Van Rompuy, insisted Lady Ashton would seek to reconcile the two sides in Kiev on the basis of "democratic rules" and aim to prevent an escalation of violence.

Earlier, in what appeared a significant concession to the opposition, Yanukovych fired his hardline prime minister, Mykola Azarov, and his government. It remains to be seen whether the pro-Russian president would seek to include opposition figures in a new government and whether the opposition would agree. The central demand from the protesters is Yanukovych's resignation and early presidential elections.

Yanukovych also caved in to pressure from the opposition, Europe and the US by promising to scrap repressive legislation passed a fortnight ago curbing freedom of speech and assembly.

The moves came after four rounds of talks between the embattled president and three opposition leaders. The laws severely curtailed freedom of assembly, with critics suggesting they in effect ushered in a dictatorship.

"We revoked the laws against which all the country has revolted," Arseniy Yatseniuk, a prominent opposition leader, said after the parliamentary vote. He called on Yanukovych to immediately sign the repeal of the legislation into law.

The street revolt against Yanukovych erupted in November after he reneged on free trade and political integration pacts with the EU, turning to Moscow which offered him $15bn (£11bn) in loans and reduced energy prices.

While Van Rompuy and the EU commission president, Jose Manuel Barroso, stressed yesterday there was no contradiction between Ukraine's agreements with Brussels and Moscow, Putin made plain that his deal with Yanukovych was incompatible with Kiev's signing up to the EU's offers.

"We would most likely fail to maintain the preferential agreements with Ukraine if it signs the [EU] association agreement," he said. He added that Moscow's deal with Kiev did not depend on the shape of the new government to be formed, but stressed that the Kremlin would need to make sure it would be able to recoup the loans.

"We can't pretend that everything's all right when it's not allright," said Barroso.

The Russians and the Europeans agreed to set up a working group of experts to discuss the detail of the agreements being offered to Kiev by Brussels. That appeared to be a concession to Moscow since it was an early demand by Yanukovych rejected by the EU in November.

Azarov, who has described protesters as "terrorists", had offered his resignation. He said he hoped the move would help achieve a peaceful resolution to the crisis that has gripped the country for more than two months.

"The conflict situation which has come about in the country is threatening the economic and social development of Ukraine, creating a threat to the whole of Ukrainian society and to each citizen," he said.

The opposition responded cautiously, saying it was unclear who would replace him.

A former Ukrainian foreign ministry official said the Kremlin was exerting huge pressure on Yanukovych behind the scenes, urging him to deal more harshly with anti-government protesters. "Ukraine is out of money. If Russia stops financing Yanukovych, he will be unable to pay his loyal supporters," the official said.

It was Yanukovych's decision to accept Russian money – and to reject a partnership agreement with the European Union – that first prompted massive pro-European street demonstrations two months ago. Radical groups have since joined the protests, which have resulted in violent clashes, at least four civilians killed and parts of central Kiev transformed into a battle zone. Dozens of activists have been arrested and several prominent leaders have disappeared. Over the weekend the government mooted the idea of imposing a state of emergency.

On Tuesday, opposition leaders said they would not abandon their uprising until their main demands were met. The demands include Yanukovych's resignation, fresh presidential elections, and an amnesty for those rounded up by police in street protests.

"It's not a victory. It's just a step towards victory," Vitali Klitschko, leader of the UDAR party and former world boxing champion, said of Azarov's resignation. Klitschko also reaffirmed his wish not to work in a new cabinet. Yatseniuk had earlier turned down an offer by Yanukovych to become prime minister. "Under no circumstances will I ever agree to work in Yanukovych's government," Klitschko said, adding that a change of prime minister would not change the government system, which needed "to get a restart".

Pro-Yanukovych politicians did not support the sacking of Azarov, who has been head of the government since 2010 when Yanukovych took power. "This will lead to additional destabilisation in the country," said Oleg Tsariov, of the ruling Party of Regions.

Parliament was due to vote late on Tuesday on an amnesty for hundreds of arrested protesters. Yanukovych sought to tie the amnesty to opposition pledges that the protest would be called off. It seems unlikely that the decisions would placate the tens of thousands of protesters and prompt them to leave the streets and destroy dozens of barricades that protect the Kiev protest camp, now known as Euromaidan (Eurosquare), from thousands of police. "I'm sure our fight will go on," said Klitschko.

The leaders of four central European EU countries bordering Ukraine are to meet in Budapest on Wednesday to discuss the crisis.