KIEV, Ukraine (AP) -- Several hundred thousand Ukrainians occupied a central square in the capital on Sunday, denouncing President Viktor Yanukovych's decision to turn away from Europe and align this former Soviet republic with Russia.

As widespread protests continued for a third week, Yanukovych's meeting on Friday with Russian President Vladimir Putin raised more fears that Ukraine is on the verge of entering a Russian-led customs union that critics say could end its economic and political sovereignty and place it back under Moscow's rule.

Ukrainian authorities have said that police won't take action against peaceful demonstrators, but concerns persist that some opposition activists may be goaded into violence.

The opposition branded Sunday's demonstration in Kiev the "march of a million," but the crowd fell short of that goal as some Ukrainians grew tired of the turmoil and others feared violence after riot police brutally beat demonstrators last weekend.

Opposition leaders, meanwhile, addressed the crowd with contradictory messages, underling the lack of a coherent plan forward among organizers.

In a letter read out by her daughter, jailed opposition leader and former Prime Minister Yulia Tymoshenko called for Yanukovych's ouster and rejected holding any negotiations with his government unless they entailed early elections. Tymoshenko is in jail on abuse-of-office charges that Western nations consider politically motivated by Yanukovych's government.

"Yanukovych has lost legitimacy as president ... he is not no longer the president of our state, he is a tyrant," Tymoshenko wrote. "Don't give in, not a step back, don't give up, the future of Ukraine is in your hands."

But her top ally, Arseniy Yatsenyuk, said a day earlier that the opposition might sit down with the government for talks if Prime Minister Mykola Azarov's Cabinet is dismissed.

World boxing champion Vitali Klitschko, another top opposition leader, also called for Yanukovych's ouster and early presidential elections, even though there is no legal possibility to impeach him and virtually no chance that he would resign on his own.

"We will fight and we are confident that we will win," Klitschko said.

Yatsenyuk focused more on ousting Azarov, punishing the police who used force against demonstrators and freeing about a dozen opposition activists arrested since last Sunday's rally. He urged demonstrators to blockade the entire government district in Kiev, the capital, which houses the Cabinet, the presidential administration and the parliament.

"We are extending our demonstration, we are going to fight until victory, we will fight for what we believe in," Yatsenyuk told the crowd, dotted by Ukrainian and EU flags.

The protest in sub-zero December temperatures took place on Independence Square, known as the Maidan, which was the site of the country's 2004 pro-democracy Orange Revolution.

"Ukraine is tired of Yanukovych, we need new rules, we need to completely change those in power," said protester Kostyantyn Meselyuk, 42. "Europe can help us."

The demonstrations began last month after Yanukovych shelved the signing of an agreement to deepen ties with the 28-nation European Union in order to focus on Russia, which worked aggressively to derail the EU deal.

During a huge demonstration a week ago, several hundred radical protesters hurled stones and attacked police as they tried to storm the presidential office, prompting a violent breakup by the authorities in which dozens were injured, including peaceful protesters, passers-by and journalists.