The Geneva agreement, signed by the United States, Russia, Ukraine and the European Union on Thursday, requires all illegal armed groups to disarm and end to the illegal occupation of public buildings, streets and squares.
Russian Foreign Minister Sergei Lavrov "did not sign anything for us, he signed on behalf of the Russian Federation," Pushilin, head of the self-declared Donetsk People's Republic, told journalists in Donetsk.
"We will persevere until the end," he said, flanked by two masked men in the occupied building of the Donetsk city administration.
Ukraine announced a military-backed operation last weekend to flush out pro-Russian rebels who have taken over state buildings including police stations in the Donbass region, though the operation faltered when pro-Russian forces seized several army troop carriers.
The diplomatic agreement in Geneva was seen as the best chance for reducing tensions in the region.
Pushilin said his men will only consider leaving public buildings when the government in Kiev, which he said was showing no signs of fulfilling its part of the Geneva deal, does the same.
"As far as vacating of buildings and areas is concerned - everyone must leave them including [Prime Minister Arseny] Yatseniuk and [acting president Oleksander] Turchinov - as they have also took them illegally," he said. "We are ready to do it after them."
Preparations for a regional referendum on increased autonomy from Kiev will go ahead as planned, he said.
"We are expecting nothing from Kiev," he said. "The date for referendum is not changing, no later than May 11."
Pushilin said any calls for pro-Russian separatists to disarm should be matched by a withdrawal of the Ukrainian military from the east Ukraine cities of Slaviansk and Kramatorsk.
"We do not want double standards," he said.