Tens of thousands of protesters joined a two-month-old encampment on Independence Square here Sunday, but speakers and demonstrators vented their frustration with opposition politicians for not providing clear leadership or a workable strategy.

Sunday’s rally was the first since President Viktor Yanu­kovych signed a package of draconian laws that restrict speech, the news media, and the right of assembly and Internet use. His action re-stoked anger among the opposition.

Looking for a fight, several hundred demonstrators armed with heavy sticks and baseball bats broke away and confronted police on the street leading up to the parliament, or Verkhovna Rada. They ignited fireworks and threw flares and stones at police officers, who responded with flash grenades and fire hoses, as the temperature dipped into the teens. There were a few pitched fights.

The Interior Ministry told the Interfax-Ukraine news agency that 20 security troops were injured, four seriously. No word was available on the number of injured protesters.

The battle pitched strident nationalists — who have been chafing at the lack of direct action — against the forces of authority. A bus was set on fire, a first for Kiev but hardly unusual in the recent history of such clashes elsewhere in Europe and around the world.

A speaker addressing the crowd at the site of the conflict said protesters were demanding that parliament — which recessed immediately after passing the legislation Thursday in a brawling, rushed session — be called back from vacation to reconsider the laws.

One opposition politician, the former boxing champion Vitali Klitschko of the UDAR party, waded into the clashes and tried to stop them, with some temporary success.

“Violence leads to nothing but mayhem,” the head of the Fatherland Party, Arseniy Yatsenyuk, told the big crowd at Independence Square, known as the Mai­dan. “With radical actions, we destroy our probable victory.”

But earlier, the crowd had chanted “Leader, leader!” to show its unhappiness with the performance of the politicians who head the three main opposition parties.

Klitschko called for a referendum on early presidential elections and said the parties arrayed against Yanukovych’s Party of Regions would begin to set up an alternative government on the grounds that the new laws were illegally hurried through the Rada.

“They should have created a provisional government months ago,” said Inna Halak, a protester from a suburb of Kiev who lost her driver’s license Saturday because she was identified by police as a participant in an auto rally against Yanukovych.

What Halak said concerns her most is that the three main opposition parties — UDAR, Fatherland and Svoboda — are starting to look out for their own interests at the expense of the movement’s. The leaders of all three parties have talked about running for president next year — or sooner, if they succeed in forcing an early vote.

The laws signed by Yanu­kovych — one of which requires advocacy groups receiving money from abroad to register as “foreign agents” — borrowed heavily from Russian legislation. If the opposition splits, that will also reflect Russia’s recent history.

Klitschko announced that he and the other two party chiefs plan to meet Monday to discuss a strategy.

That’s too late, said Halak’s friend Tamara Demchenko. “Yesterday the police took our licenses,” she said. “Tomorrow they’ll take our cars. The day after tomorrow they’ll probably take us.”

Organizers of the Maidan camp have posted a video online of the last few minutes of Martin Luther King Jr.’s final speech, in Memphis in 1968. Before his famous peroration about having been to the mountaintop, he talks forcefully about not giving in to the police or to the authorities when freedom of speech and assembly are at stake. He also takes a dig at Russia.

“We need such a leader,” Halak said.

Volodymyr Viatrovych, who has written a book on 20th-
century Ukrainian protest movements, said King, whose birthday is being observed in the United States on Monday, was inspiring because he was a spiritual as well as a political leader. Ukraine “absolutely” could use such a leader today, Viatrovych said. “And in these tough conditions, such leaders will appear.”

Others weren’t so sure that a single strong leader would solve the protest movement’s problems, but they are growing weary of the politicians. “We need to do something else. This isn’t effective. Everybody understands that,” said Natalia Starikova.

“We’re standing here for two months and no change,” said Yevheniy Pakhnyuk.

“We have no legal means” to fight back against the government, given the new laws, said his wife, Anna. “So what can we do?” Maybe, said Yevheniy, the nationalists who went off to pick a fight with the police at the Rada have the right idea.

The new laws have not been published yet, so they are not in effect. That will probably happen Monday or Tuesday. People again mocked them — especially one that makes it a crime to wear a helmet at a demonstration — by wearing all sorts of kitchen strainers and saucepans and cake plates on their heads.

Viatrovych, the historian, said the main difference between the struggle of Ukrainians to be free in the 20th century and the fight against the government today is that there is no longer any need to raise awareness of Ukraine as a nation.

“But we have to be prepared for a long fight against the authorities,” he said, though he predicted that it won’t take the 70 years that Ukrainian nationalists struggled in the previous century. “And one of the key lessons is, we don’t have to be afraid of using new methods” — or, he added, finding new leaders.