A referendum on autonomy in east Ukraine is to go ahead despite a call from the Russian president, Vladimir Putin, to delay the vote.

The co-ordinating committee of the self-declared Donetsk People's Republic announced after a meeting on Thursday that it would hold the vote on Sunday as planned. Separatists in neighbouring Luhansk announced that their vote would also go ahead.

Russian markets sank on the news, and officials in Kiev promised to press on with their campaign to retake control over the regions of Donetsk and Luhansk regardless of the rebels' decision on the poll.

"We have just voted in the People's Council … The date of the referendum was endorsed by 100% The referendum will take place on 11 May," the rebel leader Denis Pushilin said. "There are millions of people who want to cast their votes. Even if we had voted against holding the referendum, it would have happened anyway. Civil war has already begun. The referendum can put a stop to it and start a political process."

It remains unclear exactly how the vote will work, since the rebels control only fragmented pockets of the region. But rebel leaders were adamant that it would proceed. "If we don't have a referendum on the 11th then we will lose the trust of the people. We face the choice referendum or war and we choose the peaceful way" said a Donetsk People's Republic spokesperson.

On Wednesday, the Kremlin beat a tactical retreat over the regional referendum, after days of violence that left dozens dead. Overt Russian support for the plebiscite could have triggered more substantive EU and US sanctions but Putin's statement, following talks with the president of Switzerland in Moscow, looked likely to delay the imposition of harsher economic penalties.

Militia fighters in Slovyansk reacted angrily to Putin's comments. "He is a coward," said Ruslan, a self-defence guard standing in front of the city's rebel HQ. "He will pay for this with a revolution in [Moscow's] Red Square."

Many locals seemed bemused. "I don't know what's better, I just don't want war," said 40-year-old Irina standing next to a memorial to victims of the recent violence. "I wish Putin would at least arm our people."

Some said they believed that Putin was acting under pressure from the west. "It's clear that there will be world war three if Russians come here, so this is why they cannot act," said 35-year-old Andrey a member of the local self-defence militia who was wearing a black and orange striped Victory Day ribbon, a symbol of the Soviet Union's triumph over Nazi Germany. Victory Day celebrations are due to be held across the region on Friday, but some local authorities have cancelled rallies.

Moscow has also opposed the holding of presidential elections in Ukraine on 25 May – a ballot strongly supported by the west – but on Wednesday Putin sounded more conciliatory, saying the poll could be a step in the right direction.

The Russian leader insisted, however, that a presidential election should be preceded by constitutional changes in Ukraine aimed at federalising the country and handing greater powers to the regions, steps that would favour greater Russian influence over eastern Ukraine after the Kremlin annexed Crimea.

The Polish prime minister, Donald Tusk, said Nato was treating Putin's new stance with caution. "The Nato assessment, in line with ours, is that we should approach President Putin's statement with great caution," Tusk told a joint news conference with the visiting Nato secretary-general, Anders Fogh Rasmussen. "This is not yet the moment when we can announce with enthusiasm that the crisis is over. We both hope that perhaps Putin's words indicate some kind of a more optimistic scenario, but today it is too early for us to confirm that."

Rasmussen, commenting on assertions from Putin that Russian troops had pulled back from the border with Ukraine, said: "We noted the Russian statement, but up to now we have not seen any signs that the troops are actually withdrawing."

The US deputy secretary of state, William Burns, said on Thursday that Russia was heading down a "dangerous and irresponsible path" over Ukraine and that Washington and its partners would steadily step up pressure on Moscow until it changed course.

After talks with Kazakh president, Nursultan Nazarbayev, in Astana, Burns said the situation in Ukraine was "extremely combustible".

"We do not seek confrontation with Russia … but so long as Russia continues down its current dangerous and irresponsible path we will continue to work with our international partners to apply steadily increasing counter-pressure," he said.

Asked about the prospects for resolving the crisis in Ukraine, Burns said: "The short answer is: 'We'll see.'"