Ukrainian protesters have been able to enter the president’s official and residential buildings in Kiev, after they were abandoned by police.
They have stationed guards outside the entrances to offices, while the interior ministry has said in a statement that it supports the people.
President Viktor Yanukovych’s aides say he is in Kharkhiv, close to Russia.
The opposition have called for elections before 25 May, earlier than envisaged in Friday’s peace deal.
In fast-moving events on Saturday, parliament voted for opposition leader Yulia Tymoshenko to be released immediately.
She was sentenced to seven years in prison in 2011 for abuse of power. Her supporters had always maintained this was simply Mr Yanukovych taking out his most prominent opponent.
Also in parliament, speaker Volodymyr Rybak resigned, citing ill health. He has been replaced by Oleksandr Turchynov, an ally of Ms Tymoshenko.
Another Tymoshenko ally, Arsen Avakov, has been appointed interim interior minister. He replaces Vitaly Zakharchenko, who was sacked on Friday after being blamed for the deaths of civilians in last week’s crackdown on protests.
Vitaly Klitschko, leader of the opposition Udar party, repeated his demand for the president’s immediate resignation.
Meanwhile presidential aide Hanna Herman said Mr Yanukovych had travelled to Kharkiv in the east, close to the Russian border, from where he was to give a televised address.
A gathering of deputies from the south-east and Crimea – traditionally Russian-leaning areas – is taking place there, but Ms Herman said the president had “no intention” of attending, nor of leaving the country.
An opposition figure has announced to crowds in Independence Square that the president has resigned. This has not been confirmed, but the crowds reacted with huge cheers. The presidential website appears to have gone down.
‘He’s not here’
The protests first erupted in late November when Mr Yanukovych rejected a landmark association and trade deal with the EU in favour of closer ties with Russia.
Despite Friday’s EU-mediated agreement, thousands of people have remained on the streets of Kiev.
On Thursday, in the worst violence since the unrest began, police opened fire on protesters who have been occupying Independence Square in central Kiev. The health ministry says 77 people – both protesters and police – have been killed since Tuesday.
For a second day, funerals are being held in the square.
The BBC’s Kevin Bishop in Kiev says journalists and protesters were able to enter freely the previously heavily guarded presidential complex on Saturday morning.
The protesters have not entered the offices themselves. They said they were protecting the buildings from looting and vandalism.
“He’s not here, none of his officials or anyone linked directly to the administration are here,” said Ostap Kryvdyk, a protest leader, referring to the president.
Correspondents say police appear to have abandoned posts across the city, while the numbers gathered in Independence Square – known as the Maidan – are growing.
Hundreds of people have also entered the grounds of the president’s official residence, the Mezhyhirya, about 15km (10 miles) north of the city centre.
In a statement, the interior ministry said the police force was “at the service of the people and completely shares its aspirations for rapid changes”.
“We pay homage to the dead,” it added.
The political pact was signed on Friday by President Yanukovych and opposition leaders after mediation by EU foreign ministers.
It restores the 2004 constitution – which reduces the powers of the presidency – and says a unity government will be formed and elections held by the end of the year.
The deal has been met with scepticism by some of the thousands of protesters who remain in the square. Opposition leaders who signed it were booed and called traitors.
The US and Russian presidents have agreed that the deal needs to be swiftly implemented, officials say.
Russia’s Vladimir Putin told Barack Obama in a telephone conversation on Friday that Russia wants to be part of the implementation process, a US State Department spokesperson said.
Shortly after the deal was signed, Ukraine’s parliament approved the restoration of the 2004 constitution, which reduces the powers of the president.
All but one of the 387 MPs present voting in favour, including dozens of MPs from Mr Yanukovych’s own Party of Regions.