Many Ukrainians resent Russia's centuries of political control of Ukraine and the pressure it has exerted since the 1991 collapse of the Soviet Union.
The EU wants to pry away Ukraine from Russia's orbit, while Moscow aims to get Kiev to join a union that would rival the European bloc.
"Russia has shown that it remains an imperialist country that is pulling Ukraine into the Soviet past, and Yanukovych is helping with this," said protester Vladimir Mikolaychuk, a 50-year-old businessman.
The EU summit, which Yanukovych is attending, continues Friday, but officials appeared to have little hope that Yanukovych could be persuaded to sign.
If the summit concludes without signing the agreement, the protests could grow larger and more vehement. The mass protests of 2004 known as the Orange Revolution forced the rerun of a fraudulent presidential election in which Yanukovych was credited with the most votes. His opponent Viktor Yushchenko won the revote, but Yanukovych gained the presidency in 2010 and is wary of a possible repeat of huge protests.