DONETSK, Ukraine (AFP) - Pro-Moscow rebels fighting in east Ukraine vowed on Thursday to press on with a disputed independence referendum, ignoring a call from President Vladimir Putin to postpone the vote in a bid to ease tensions.

"The vote will happen on May 11," the leader of the self-proclaimed People's Republic of Donetsk, Denis Pushilin, told reporters.

A rebel spokeswoman in Slavyansk confirmed to AFP the vote would also take place there, despite a Ukrainian military operation to besiege the flashpoint town.

The move reignited the crisis in Ukraine after Putin on Wednesday made a surprise call to the rebels to postpone their referendums and backed a previously disparaged presidential election planned by Kiev's interim leaders on May 25.

On Thursday, Cold War-style tensions surged again to the fore, with Russia test-firing ballistic missiles while its defence minister stressed the country's nuclear capable forces remained on "constant combat alert".

Putin had set as a condition for pushing back the referendums that the military operations waged against the rebels by the pro-Western government in Kiev must end.

After initially being caught off guard by Putin's appeal, the rebels on Thursday rejected the Russian leader's proposition after holding consultations.

"The date of the referendum will not be postponed," Pushilin said.

An identical referendum has also been called for the neighbouring eastern region around the city of Lugansk. There was no immediate word whether Lugansk's rebels were maintaining their referendum.

One Slavyansk resident who gave his name as Sergiy told AFP the referendum "must go ahead as soon as possible before the presidential election".

"Whatever happens, I'll go and vote. It seems the majority of the population is in favour of federalisation." And Kiev vowed to press ahead with what it calls an "anti-terrorist" operation against insurgents holding a dozen or so towns and cities in the east.

"The counterterrorist operation will go on regardless of any decisions by any subversive or terrorist groups in the Donetsk region," Andriy Parubiy, secretary of Ukraine's national security and defence council, told reporters in Kiev.

Prime Minister Arseniy Yatsenyuk said in a speech marking the Soviet victory against Nazi Germany that Ukraine was facing "a real albeit undeclared war".

Putin had also said Wednesday after his meeting with OSCE chair and Swiss President Didier Burkhalter that Russia had withdrawn its estimated 40,000 troops from the Ukrainian border.

But NATO Secretary-General Anders Fogh Rasmussen told reporters in Warsaw he had yet to see "any indications" that Russia had actually done so.