Ukrainian police have used tear gas in fresh clashes with pro-EU activists in the heart of Ukraine's capital Kiev.
Reports say some protesters tried to enter the government building but were pushed back by police.
Thousands of protesters gathered on European Square again after a huge rally on Sunday - the biggest since the 2004 Orange Revolution.
They are angry at the government's decision not to sign a major trade and association deal with the EU.
In recent weeks the government has come under Russian pressure not to sign the pact, but to join a Russian-led customs union with former Soviet states instead.
Opposition leaders, including world heavyweight boxing champion Vitali Klitschko, called the government's decision "shameful" and vowed to keep up mass protests in central Kiev indefinitely.
The activists included supporters of jailed opposition leader Yulia Tymoshenko, who urged the government to release her - a plea that has also been made by EU politicians.
Ms Tymoshenko wants to get treatment in Germany for chronic back pain and the EU has made her release a key condition for signing the pact with Kiev. But last week Ukraine's parliament rejected legislation that would have enabled her to go.
More than 100,000 people rallied in Kiev on Sunday, the opposition said. Police estimated the crowd at about 50,000.
Hundreds of protesters stayed in tents on the square overnight, despite an order from the authorities not to do so.
Tents were a big feature of the pro-Western Orange Revolution, which challenged Russia's traditional influence in Ukrainian politics.
Viktor Yanukovych is president now, having been elected in 2010, but back in 2004 he was toppled by the Orange Revolution after an election widely condemned as fraudulent.
The authorities have launched criminal proceedings against some activists who clashed with police on Sunday.
The Interfax-Ukraine new agency said several hundred protesters gathered outside the government building on Monday and various objects "started flying in the direction of the police", prompting the police to don gas masks and form a human chain.
Some activists told a BBC reporter at the scene that there were athletic-looking young people in the crowd whom they suspected of being agents provocateurs.
In addition to Vitali Klitschko, opposition leaders Arseniy Yatsenyuk and Oleh Tyahnybok addressed the crowd. They urged President Yanukovych to sack Prime Minister Mykola Azarov and to sign the association agreement with the EU.
The signing had been set for 29 November in the Lithuanian capital Vilnius, where several other ex-Soviet states will forge closer ties with the EU.
Russia has threatened unspecified economic measures if Ukraine signs the deal with the EU. In the past Moscow has suspended gas supplies, in disputes over prices, and this year it blocked imports of Ukrainian chocolates.
Russia has also boycotted wine and mineral water from Georgia and Moldova - two other ex-Soviet states seeking favourable trade terms with the EU.
In television interviews on Sunday Mr Azarov accused the EU and International Monetary Fund of failing to offer Ukraine enough financial support.
He told Russian TV a letter from the IMF had been "the last straw" because the fund had linked the granting of a credit to "conditions that were absolutely unacceptable to Ukraine, such as raising the tariffs for housing and utilities, freezing wages and pensions".
On the EU, he said :"We are being told: you carry on working and carry on moving forward but don't expect any money.
"So far we have only been given a verbal promise that in the next seven years Ukraine can expect 1bn euros [£835m; $1.3bn]. And what is 1bn euros? It is nothing," he said.
Ukraine depends on imports of Russian gas, but recently the supplier, Gazprom, complained that Ukraine had fallen behind in payments. Pipelines transiting through Ukraine pump Russian gas to many EU member states.
Mr Azarov told Ukrainian TV that Russia had promised to review the terms of its gas sales. However, Gazprom later denied that there was any such promise.