Many demonstrators also marched on President Viktor Yanukovych’s official residence outside the capital.
They have been re-energised by a brutal attack on a prominent journalist, Tetyana Chornovol, on Christmas Day.
She had accused Mr Yanukovych of corruption over his financing of the Mezhygirya residence in an expose.
Mr Yanukovych denies any allegation of corruption and has called for an investigation into the attack on Ms Chornovol.
“We plan to come out here until the day the authorities make changes to the constitution and limit the powers of the president,” Kiev pensioner Tetyana Kornienko told AFP news agency, amid a sea of Ukrainian flags fluttering across Independence Square.
Protesters then made their way to the Mezhygirya residence, some 15km (nine miles) away on the banks of the Dnipro river, by bike, car and minibus, where they carried a coffin to symbolise what they hope is the end of his political life, AFP reported.
They were kept several hundred metres from the heavily guarded residence.
Demonstrators first took to the streets in late November, angered by President Yanukovych’s decision to abandon an association agreement with the European Union in favour of closer ties with Russia.
Protesters continue to occupy the central Independence Square and have refortified barricades to ward off attempts by police to clear the camp – though such attempts now appear to have been abandoned.
But until Sunday their demonstrations had been dwindling in size since they started last month, and there were fewer people on the streets on 22 December than in previous rallies, says the BBC’s David Stern in Kiev.
They appeared to be undermined by a deal Ukraine struck with Russia on 17 December, under the terms of which Russia bought $15bn (£9.2bn; 10.9bn euros) of Ukrainian government bonds.
The deal also saw the price of imports of natural gas on which Ukraine’s precarious economy depends slashed by a third.
But on Sunday, more protesters returned to the streets of Kiev, many angered by the attack on Ms Chornovol, who says her car was run off the road before she was taken out and beaten by men.
Graphic pictures have been circulated of her bloodied and swollen face following the beating.
Local news agencies say five men have been placed under arrest but no motive has been put forward.
Ms Chornovol says her assailants followed her in a “black luxury” SUV after she had been taking pictures of the residences of senior administration figures.
“When you are struck by a luxury car, you understand that a price has been put on your life,” the 34-year-old told pro-opposition Channel 5 television from her hospital bed, according to AFP.