Yanukovych turned on the "irresponsible" opposition which has refused to abandon more than two months of protests despite a string of concessions, including an amnesty for jailed demonstrators.
The street rallies first erupted when the president backed out of a key pact with the European Union in November in favour of closer ties with Moscow, but the unrest has since spiralled into an all-out uprising for the president's removal.
In the latest twist to the saga, Yanukovych's office on Thursday announced the leader had fallen ill with an "acute respiratory infection".
The president's sick leave came after a fraught parliament session on Wednesday night where he had to personally intervene to prevent a possibly decisive schism in his ruling Regions Party.
The upheaval has raised fears of a new point of discord between Russia and the West, with Russian President Vladimir Putin urging the European Union not to meddle but Western states hugely critical of Yanukovych's rule.
Ukraine's first post-independence president Leonid Kravchuk on Wednesday warned that the country was "on the brink of civil war".
Thousands of protesters were on Thursday still occupying much of Kiev's city centre, including radical activists in balaclavas who patrolled the barricades carrying crowbars.
Clashes between protesters and security forces last week left three activists shot dead and turned parts of the capital into a battlefield, in the country's worst unrest since its independence in 1991.
Hours after his sick leave was announced, Yanukovych issued a defiant statement accusing the opposition of behaving irresponsibly by not calling off the protests.
"The opposition is continuing to inflame the situation and is calling on people to stand in the freezing cold due to the political ambitions of several leaders," he said in a statement on the presidential website.
He said the opposition was making "ill-considered and irresponsible announcements, thinking about their own ratings more than the life and health of people."
But in a rare show of contrition, Yanukovych also admitted he needed to take more account of the country's mood.
"From my side, I will show more understanding for the demands and ambitions of people, taking into account the mistakes that authorities always make."
Yanukovych has already granted several concessions to the protesters, including accepting the resignations of Prime Minister Mykola Azarov and the entire cabinet, as well as allowing the annulment of tough anti-protest laws.
Ukraine's parliament, with backing from the ruling Regions Party, late on Wednesday passed a bill that would offer an amnesty to arrested protesters.
But the opposition defiantly refused to take part in the vote because the amnesty is conditional on protesters leaving occupied streets and buildings 15 days after it comes into force.
According to prosecutors, four people have died and 234 people have been arrested across Ukraine in the protests.
The amnesty would apply to all those detained save those accused of grave crimes.
Facing a rebellion within the Regions Party where some 40 MPs had threatened to side with the opposition, Yanukovych had visited parliament late Wednesday in a bid to bring them back into line.
Reportedly threatening early elections and swearing liberally, Yanukovych's intervention ensured that the law was adopted by the majority.
But the three main party leaders -- Svoboda (Freedom) party leader Oleg Tyagnybok, UDAR (Punch) party leader and world boxing champion Vitali Klitschko as well as Fatherland party leader Arseniy Yatsenyuk -- condemned his move as violating the constitution.
"Through blackmail and intimidation, he compelled his party, which is on the verge of splitting, to return to the chamber and adopt the law despite not having enough votes," they said.
Russia watches, Ukraine economy fragile
Following complaints from Ukrainian companies, the Russian customs service was on Thursday forced to deny claims that Moscow had introduced tighter border checks, a tried-and-tested method of pressuring Kiev in the past.
The Federation of Employers of Ukraine, a lobby group, said on Wednesday that Russian customs had introduced "rigorous" checks on Ukrainian-made foodstuffs, machinery, metals and trading equipment.
Ukraine remains mired in deep economic trouble and has accepted a $15-billion bailout from Moscow, though Russia this week warned that further payments will only be released when a new government is named.
Ukraine saw zero growth last year after nine months of economic declines were followed by a strong fourth quarter, the statistics committee said on Thursday.