(CNN) Ukraine Ukrainian Prime Minister Mykola Azarov said Tuesday the government was "open to dialogue" with the opposition demanding his ouster, but that if the offer is met with "a fist, I say frankly -- we have enough forces." He made the remarks in parliament, the government website said.
The Ukrainian opposition failed to topple the government in a no-confidence vote Tuesday, but thousands of protesters stayed put in the streets, upping pressure on President Victor Yanukovich.
Despite failing in parliament to force the resignation of the Cabinet, opposition leaders remained undeterred in their demands for new elections in the Eastern European country, calling on Yanukovich himself to sack the Prime Minister and his government by executive order.
Earlier, in the tightly secured parliament in Kiev, opposition lawmakers garnered 186 votes after tabling the motion. They needed 226 votes to bring the government down.
Ukraine has plunged into crisis in recent days after Kiev's last-minute decision not to sign a historic political and trade agreement with the European Union, sparking mass rallies.
Tens of thousands of protesters descended onto the capital's Independence Square to voice their anger over the weekend, and demonstrations spilled over into Monday when they blocked the government's main headquarters with trash bins and containers, preventing employees from going to work.
Braving the cold weather, many set up tents and remained in the square, waving flags and chanting against the government in the biggest protests in Ukraine since the 2004 Orange Revolution -- a massive populist movement that booted Yanukovich, then Prime Minister, from office.
"The protests will go on until the opposition finds a way to solve this," protester Sergey Vysotsky, 24, told CNN.
"My guess is that they (the demonstrators) won't go back to their homes until they accomplish what they came here for."
Their numbers continued to swell Tuesday, with one large group remaining in the square and another marching toward the President's administration building after the vote. Their anger was evident.
"Well, if they (the government) are not following the will of the nation, they are illegitimate," demonstrator Yehven Buleha, said. "We need to create our own government and introduce our order, our right to vote."
The protests have mainly been peaceful, but violence broke out Sunday when demonstrators tried to push through barricades at the President's administration building using a bulldozer. They were met with stun grenades and tear gas.
Then, after dark, the batons came out; police chased and beat protesters. Dozens were hurt on both sides.
Yanukovich, who left for China on Tuesday, broke his silence Monday, telling reporters that he supports a peaceful resolution to the "questions brought on by our citizens."
"As for the politicians participating in this, I consider any radicalization of the political process will only have negative consequences," he said. "And using civil rallies with the aim of radicalization is always a mistake, and someone must always carry political responsibility."
Opposition leaders have been calling for new parliamentary and presidential elections. There was a heavy security presence outside the parliament, where protesters, who on Monday blocked streets and called for a general strike, waved Ukrainian and EU flags.
Despite the parliamentary vote not going the way it wanted, the opposition made clear it would not back down.
Opposition leaders Vitaly Klitschko and Arseniy Yatsenyuk called on Yanukovich to sack the Prime Minister and his government by executive order. Klitschko, who gained fame as a boxer, vowed that the opposition would stay out in the streets to make sure their demands were met.
Prime Minister Mykola Azarov has said the government was being blocked from performing its basic functions, which could affect the payment of pensions and salaries.
"People are being directed to capture government buildings, to block the work of government institutions, to put forward ultimatums. It's a path leading to nowhere."
Ukraine's central bank said it would seek to uphold financial stability in light of the protests. In a video statement, National Bank of Ukraine chairman Ihor Sorkin urged depositors to be confident in the banking system and not withdraw their savings.
Ukraine is split between pro-European regions in the west of the country and a more Russia-oriented east
At the heart of the protests is Ukraine's about-turn after a year of insisting that it was intent on signing a historic political and trade agreement with the European Union.
The deal, the EU's "Eastern Partnership," was aimed at creating closer political ties and generating economic growth among the nations of Eastern Europe and the Caucasus, including Ukraine, Moldova, Georgia, Armenia, Azerbaijan and Belarus.
On November 21, Yanukovich's government decided to suspend talks with the EU, angering Ukrainians.
The agreement with the EU would have opened borders to trade and set the stage for modernization and inclusion, they said.
Yanukovich had his reasons for backpedaling on the deal. Chief among them was Russia's opposition to it.
Russia threatened its smaller neighbor with trade sanctions and steep gas bills if it forged ahead.
If Ukraine didn't, and instead joined a Moscow-led Customs Union, it would get deep discounts on natural gas, Russia said.
Yanukovich was also facing a key EU demand that he was unwilling to meet: Free former Prime Minister Yulia Tymoshenko, his bitter political opponent. The Orange Revolution that swept him from office also swept Tymoshenko to power.
Two years ago, she was found guilty of abuse of office in a Russian gas deal and sentenced to seven years in prison in a case widely seen as politically motivated. Her supporters say she needs to travel abroad for medical treatment.
Russian President Vladimir Putin dismissed the protests Monday, saying they are unrelated to Ukraine's turn away from the European Union. He called them reminiscent of a "pogrom" rather than a revolution and an effort by the opposition to destabilize the government, according to Russia's state news agency RIA Novosti.
"These actions are, in my opinion, prepared not in view of current events, but for the 2015 election campaign," Putin said.
In an interview with CNN's Christiane Amanpour on Monday, Yatsenyuk, leader of the Motherland opposition party, said the demonstrations were "like a legacy of the Orange Revolution."
"Due to the Orange Revolution, people have the spirit of freedom in my country," he said.
The European Union, Yatsenyuk said, was "very clear" that signing a trade deal would not be an auction.
"You can't sell the country to the European Union or to Russia," he said. "This is the way how to reform the country."
Facing a worsening crisis on the streets, Yanukovich on Monday asked the European Commission to receive a Ukrainian delegation for talk on "some aspects" of the agreement Kiev had been expected to sign, according to a statement from Brussels.
Commission President Jose Manuel Barroso agreed to the request but added that the commission was ready to discuss implementing "agreements already initialed, but not to reopen any kind of negotiations."