Armed pro-Russian separatists in eastern Ukraine have said they are not bound by an international deal ordering them to disarm.

They also said they were looking for more assurances about their security before leaving the public buildings they are holding.

Yesterday’s agreement brokered by the United States, Russia, Ukraine and the European Union offered the best hope to date of defusing a stand-off in Ukraine that has dragged East-West relations to their lowest level since the Cold War.

Ukraine said it was preparing a law to give the separatists amnesty, although the drive to root them out would continue.

The agreement requires all illegal armed groups to disarm and end occupations of public buildings, streets and squares.

But with the separatists staying put in the east and Ukrainian nationalist protesters showing no sign of leaving their camps in the capital's Maidan Square, it was not clear which side would be willing to move first.

Enacting the agreement on the ground will be difficult, because of the deep mistrust between the pro-Russian groups and the Western-backed government in Kiev, which this week flared into violent clashes that killed several people.

Russian President Vladimir Putin overturned decades of post-Cold War diplomacy last month by declaring Russia had a right to intervene in neighbouring countries and by annexing the Black Sea peninsula of Crimea.

The move followed the overthrow of Ukraine's pro-Moscow president Viktor Yanukovych, after months of street protests prompted by his rejection of a trade deal with the EU.

The fact any deal was reached at all in Geneva yesterday came as a surprise.

It was not clear what had happened behind the scenes to persuade the Kremlin, which had shown little sign of compromise, to join calls on the militias to disarm. Russia rejects Ukrainian and Western accusations of orchestrating the gunmen.

In Slaviansk, a city that has become a flashpoint in the crisis after men with Kalashnikovs took control last weekend, leaders of the pro-Russian groups met inside one of the seized buildings to decide how to respond to the Geneva agreement.

Anatoly, one of the armed separatists who have taken over police headquarters, said: "We are not leaving the building, regardless of what statements are made, because we know what is the real situation in the country and we will not leave until our commander tells us to."

Two Ukrainian military aircraft circled Slaviansk several times today.

In front of the mayor's office, men armed with automatic rifles peered over sandbags, which had been piled higher overnight.

Separatists remained in control of the city's main streets, searching cars at checkpoints around the city.

The self-declared leader of all the region's separatists said he did not consider his men to be bound by the agreement.

Russian Foreign Minister Sergei Lavrov "did not sign anything for us, he signed on behalf of the Russian Federation," Denis Pushilin, head of the self-declared Donetsk People's Republic, told journalists in Donetsk, the regional capital.

First, he said, the prime minister and acting president who took power in February should quit their offices, as they took them over "illegally".

But Alexei, another separatist in Slaviansk acknowledged that the Geneva talks had changed the situation.

"It turns out Vova doesn't love us as much as we thought," said Alexei, using a diminutive term for Mr Putin, who is viewed by many of the separatist militias as their champion and protector.

In the capital, Kiev, people on the Maidan, the local name given to Independence Square which was the centre of protests that eventually toppled Mr Yanukovych, said the barricades would not come down until after the 25 May presidential election.

Prime Minister Arseny Yatseniuk told parliament he was not overly optimistic about the agreement, but said Russia had been "forced" to call on the "illegal armed groups" to surrender.

US President Barack Obama said the meeting in Geneva was promising, but that the United States and its allies were prepared to impose more sanctions on Russia if the situation fails to improve.

"There is the possibility, the prospect, that diplomacy may de-escalate the situation," Mr Obama told reporters.

"The question now becomes, will in fact they use the influence they've exerted in a disruptive way to restore some order so that Ukrainians can carry out an election and move forward with the decentralisation reforms that they've proposed," he said at the White House.

Ukraine's government promises to devolve power to regions and protect people's rights, notably in the east, to use the Russian language in public life.

But it rejects calls for a federal structure, which it says could lead to permanent Russian interference in the east and eventually break up the country.

US Secretary of State John Kerry said in Geneva that if by the end of the weekend there were no signs that pro-Russian groups were pulling back, there would be costs for Moscow, a reference to further EU and US sanctions.