Stun grenades and flares were thrown as groups of people headed for parliament, which was cordoned off by rows of police and buses.
Opposition politician Vitali Klitschko tried to stop attacks on police.
The laws were passed with a quick show of hands on Thursday by MPs loyal to President Viktor Yanukovych.
The opposition accused the ruling party of a coup.
US and EU officials have expressed deep concern at the new legislation.
Ukraine’s current anti-government movement began in protest at Viktor Yanukovych’s decision in late November to pull out of a landmark treaty with the EU, but has expanded to demand his resignation.
Sunday’s rally in Kiev, attended by tens of thousands, heard calls from opposition politicians to disregard the new laws curbing protests that pro-EU demonstrators have been staging for the past two months.
Clashes erupted as some people headed away from the main square towards parliament, encountering cordons set up by police. Live TV pictures showed them attempting to overturn a bus used by police. The bus was set on fire after petrol bombs were thrown.
Interior Ministry spokesman Serhiy Burlakov blamed “provocateurs and extremists” for the confrontations and urged people not to follow their lead.
Police were filming everything and had opened criminal proceedings under Article 294 (organization of mass riots), the Interior Ministry said.
Earlier the rally on the main square heard a call from a former Ukrainian navy chief for members of the armed forces to defy “illegal” orders from those in power, Unian news agency reported.
Rear Adm Ihor Tenyukh, who was sacked by President Yanukovych in 2010, warned of the dangers posed by the “coup d’etat planned by the current authorities”.
“Tomorrow the regime will enslave you too. Therefore we are calling on you to fulfill your military oath of loyalty to the Ukrainian people and not to the authorities who have gone off the rails,” he was quoted as saying.
Opposition leaders are under huge pressure to come up with an action plan, amid criticism from many activists that their campaign has been too passive.
The new curbs on protests, which have been signed into law by the president, include:
The protesters have been camping out behind extensive barricades on the Euromaidan, as Independence Square has been dubbed, for nearly two months.
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