Hours later, after nightfall, the protests were continuing, with many people still on the square and many thousands more trying to block off government buildings nearby.
The opposition had called on Ukrainians to turn out to express anger with Yanukovych and call for his removal, hoping to surpass the 300,000 or so who took to the streets a week ago.
Authorities meanwhile have said a criminal investigation has been opened targeting unnamed politicians who they said were trying to usurp government power.
Many protesters remained camped out on the square, waving blue-and-yellow Ukrainian flags, singing songs and sharing hot beverages in small groups, and listening to opposition appeals broadcast over loudspeakers.
Tens of thousands more were on the move, clogging junctions leading to the nearby government district, according to RFE/RL's Ukrainian Service.
They appeared to be responding to an opposition call to block off the government district, with some vowing to continue to demonstrate until new parliamentary and presidential elections were called.
The neighborhood includes the parliament, presidential administration, and government headquarters. Demonstrators were setting up protest tent camps on the streets and erecting barricades well after nightfall as the area being blocked continued to grow.
"To be honest, it's a little bit scary to walk the streets," one female protester told RFE/RL's Ukrainian Service. "But you can feel the spirit, you can feel that there are a lot of us. And if we are together -- we are the power -- and everything is going to be alright."
Another protester expressed conviction but hinted at doubts over extent of demands being issued.
"In my opinion, the demands are good, but we must put pressure on the authorities to fulfill these demands -- the resignation of the government -- yes, the resignation of the president," the man said. "I have doubts about early elections, but in this case we also must put pressure and demand to do so."
Protesters toppled a Lenin statue in downtown Kyiv.
Vitali Klitschko, the leader of the opposition Udar (Punch) party, had claimed that "nearly a million" turned out for the daytime rally.
Police estimated the turnout at more than 60,000.
Earlier, RFE/RL correspondent Tom Balmforth spoke with protesters who said they had organized to prevent the kind of violence that might provide a "pretext" for authorities to break up the gathering, as happened a week ago.
He said a mood of defiance was thick in the air.
Jailed former Prime Minister Yulia Tymoshenko, in a letter read out to the gathering by her daughter, called for Yanukovych's ouster, saying he "has lost legitimacy as president."
Tymoshenko, who was imprisoned on abuse-of-office charges the opposition and many Western leaders say were politically motivated, also said Yanukovych is "no longer the president of our state, he is a tyrant."
"Right now we are living through the most difficult historical period of all the 22 years of our independence," Yevhenia Tymoshenko told demonstrators. "We are are walking down a razor's edge, between the complete collapse into a brutal dictatorship and the return home to a European community."
The crowd chanted "Europe! Europe!" in response.
Arseniy Yatsenyuk of Tymoshenko's Batkivshchyna party vowed to expand the protests and urged demonstrators to blockade the entire government district in the capital.
"[Yanukovych] thinks that we will not stand here very long," Yatsenyuk told the crowd, "but we know that there will be more of us. We stand firm in the fight for our rights and with every coming day we will only broaden our action."
Klitschko echoed that call for Yanukovych's ouster and early presidential elections.
The demonstrations, which have produced the largest public outpouring of anger since the country's Orange Revolution in 2004, in which Yanukovych arch rival Tymoshenko played a leading role, are well into their third week.
Ukrainians and Western backers of the country's further integration with Europe are concerned that Yanukovych's tack will steer the country back into a subservient relationship with Russia.
Yanukovych and his allies shocked Brussels and the pro-EU Ukrainian public with their decision to suspend talks abruptly on an Association Agreement with Brussels in order to assess its effect on relations with Russia.
A similar protest on Independence Square on December 1 attracted about 300,000 protesters, the biggest demonstration in Ukraine since 2004.
Clashes between a group of radical protesters and police one day earlier had prompted a violent police crackdown in which dozens were injured.
Early on December 8, RFE/RL correspondent Balmforth said there was virtually no police presence in the center of Kyiv, and opposition demonstrators filled Independence Square and nearby streets.
But riot police were still guarding the presidential administration building, he said, where thousands of protesters also took up positions outside.
A spokeswoman for Ukraine's Security Service on December 8 said the service had opened a criminal probe into alleged attempts by "certain" politicians to seize state power. She did not name the politicians.
RFE/RL's correspondent spoke with a group of protesters who had organized themselves and were patrolling the area in ranks -- equipped with helmets and makeshift body armor -- in an effort to prevent "provocateurs" from attacking government buildings, which they said would provide a pretext for authorities to attack them.
On December 7, former Georgian President Mikheil Saakashvili addressed some 20,000 protesters in Kyiv, urging them to continue their demonstrations to bring their country closer to Europe.
"I am Ukrainian, I am Georgian, and I am a European," Saakashvili told the crowd, some of whom have been camping out since a summit in Vilnius on November 29 at which Ukraine had originally been hoping to initial the EU deal and where Georgia initialed its Association Agreement. "I knew that one day Ukraine would become an example of success, an example of an Eastern European nation integrated into the European family of free, democratic, prospering countries. Today I see that I was right. Ukraine will be able to do this, we will do this together."
The same day, former Moldovan Prime Minsiter Vlad Filat -- whose country similarly initialed an Association Agreement in the Lithuanian capital -- told RFE/RL that the atmosphere in Ukraine is tense but that it is a time for dialogue.
"What is important now, during this time period, is to respect the will of the Ukrainian citizens and their will is clearly expressed in favor of the pro-European values [of closer ties to the European Union]," Filat said. "For Moldova, it is vital that Ukraine goes further in this European integration process so that together we can improve the lives of our citizens. That's why we were, we are, and we will be united and show solidarity with the process of the European integration of Ukraine."
An unwilling ruling party and Yanukovych's decision to defer to relations with Russia led to Ukraine's signing ceremony being canceled at the Vilnius event.
Tensions between Brussels and Kyiv had also increased recently over the continued jailing of Tymoshenko.
Both Moscow and Kyiv have denied reports that Yanukovych and Russian President Vladmir Putin on December 6 discussed Ukraine joining a Russian-led customs union. A Putin spokesman said the two had focused on "cooperation in the energy sphere."
Opposition leader Yatsenyuk called such a customs union "a new version of the Soviet Union."
The demonstrators are demanding the ouster of the government, new elections, and the punishment of police responsible for violence against demonstrators.
They face a court-ordered deadline of early next week to end their blockade of government facilities.