Pro-Russian separatists in eastern Ukraine vowed Thursday to press ahead with a referendum on independence, defying Russian President Vladimir Putin’s surprise call for Sunday’s vote to be postponed.

Having captured government buildings across eastern Ukraine and vehemently denounced the interim government in Kiev as fascists, the leaders of the self-styled Donetsk People’s Republic argued that they would lose credibility if they canceled the vote.

“Civil war has already begun,” Denis Pushilin, a prominent leader of the group, said at a packed news conference in Donetsk. “The referendum can put a stop to it and start a political process.”

[READ: Who are these men defying both Putin and Kiev?]

The decision to proceed with the vote could be seen as a rebuff to Putin, whose call Wednesday for a postponement struck a more conciliatory tone than his previous statements on Ukraine.

Footage from RT shows Russia test-launching missiles during military drills Thursday.

It remained unclear what a referendum might look like, who would participate, how fair it might be, or even in how many or which cities it would be held.

But the separatists clearly felt they had little choice but to press on: Canceling the vote would leave them without even a fig leaf of popular legitimacy and deflate their movement, perhaps fatally.

Ukraine’s acting prime minister, Arseniy Yatsenyuk, said Thursday that any referendum would lack legitimacy. Ukraine has said questions about the country’s future should be decided in a nationwide presidential election scheduled for May 25, not in any regional vote.

Feeding a sense that the let-up in tensions had been fleeting, Putin on Thursday led major military exercises that simulated a response to a massive attack on Russian soil, defense officials in Moscow said.

Kremlin-backed television channels showed vast salvos being fired across Russia, including intercontinental ballistic missiles from submarines, cruise missiles from a Tupolev bomber and scores of Grad rockets raining down on a practice range.

Putin said the strikes were part of exercises that were planned in November to demonstrate the high readiness of the country’s “strategic offensive and defensive forces.”

The separatists called the referendum to decide whether the Donbas region of eastern Ukraine, the nation’s industrial heartland, should declare independence.

But with little coordination or trust among separatist leaders in different cities across the region, it was far from clear what a putative new republic would look like.

There was also widespread skepticism about the separatists’ ability to stage a referendum with even a minimum of credibility.

Boris Litvinov, a leader of the referendum effort, said that about 3 million ballots have already been printed and 2.7 million of them distributed. The ballots ask voters whether they support the “independence of the Donetsk People’s Republic.”

But he said authorities in Kiev have denied the separatists access to voter rolls. Therefore, he said, the referendum would be an “open process” in which people would simply turn up at polling centers, show their passports, sign their names and cast their ballots.

After two days of mixed messages from Russia, Putin’s real intentions about the referendum remained hard to read. Analysts in Moscow said he could be playing a double game, disassociating Russia from what is likely to be a deeply flawed contest while maintaining flexibility in how to respond.

“Russia is trying to distance itself from the separatists, but if referendums are held, Russia might be able to benefit from them,’’ said Alexei Makarkin at the Moscow-based Center for Political Technologies.

The Pentagon and NATO continued on Thursday to dismiss a claim by Putin that Russian troops had been pulled back from the Ukrainian border. The disagreement sparked a Twitter spat Thursday between the Russian Foreign Ministry and NATO Secretary General Anders Fogh Rasmussen, who said he had seen no sign of a withdrawal.

In the streets of Donetsk, confusion reigned Thursday about what the vote really means, and there appeared to be agreement on only one thing: People want peace and stability to return.

Many residents feel that democratically elected president Viktor Yanukovych, who fled the country in February, was ousted illegally through street protests. To them, the interim government in Kiev that replaced him does not represent people in the mainly Russian-speaking east and is in league with Ukrainian ultranationalists.

But people expressed a wide range of views on the best way forward, which the yes-no question posed by the referendum will not be able to capture, and few seemed to want to become part of Russia.

Indeed, polls show that most people in eastern Ukraine want the country to stay together, although many would like greater autonomy.

A 31-year-old doctor who gave her name only as Tatyana — like others interviewed, she declined to give her full name — said she would not vote. “I have not received any invitation or information,” she said while walking her baby in a stroller. “And even if I wanted to give my opinion, I am afraid of the men with guns.”

Three men chatting on a street corner expressed indifference toward the whole process, which they said described as maneuvering by political leaders and business magnates that did not concern them. “We can’t do anything; our voice does not matter,” said Zhenya, a 29-year-old warehouse worker.

A group of construction workers who were having a drink after work near the city’s central market said they support the referendum because they want their region to be independent of Kiev. But they said they do not want to join Russia.

“There is a lot of antagonism toward Kiev, but there is a still a lot of support for Donbas staying in a united Ukraine,” said Adam Swain, an associate professor at the University of Nottingham who was visiting Donetsk and has been conducting economic research in Ukraine for two decades.

Separatist leaders said there was still room for negotiation or even postponing the referendum if Kiev withdrew its troops from the region. But they said that if a majority votes yes in the referendum, they would proclaim independence. The question of whether to join Russia would come later, they said.

“The only negotiation with Kiev will be for them to withdraw their troops,” Litvinov said.

Birnbaum reported from Moscow and Kunkle from Kiev. Alex Ryabchyn in Donetsk and William Branigin in Washington contributed to this report.