Yanukovych, who has been wrestling with nearly two months of opposition protests, signed off Friday on tough new laws introducing jail time and corrective labour for those occupying public buildings or disseminating slander on the Internet.
But the opposition pushed ahead with plans to hold a fresh rally Sunday, reinforcing their barricades in the capital with barbed wire and planks.
Critics say Yanukovych has followed in the footsteps of Russian President Vladimir Putin, who pushed through similar legislation after returning to the Kremlin for a third term in 2012 following huge protests against his decade-long rule.
"There is only one question left after newly signed laws - quo vadis (where are you going) Mr President?" EU Commissioner for Enlargement and European Neighbourhood Policy Stefan Fule asked Yanukovych on Twitter.
The United States and European Union have called the laws anti-democratic, while the opposition accused the president of seeking to install a "dictatorship".
At the height of the protests last month hundreds of thousands took to the streets after Yanukovych's decision to ditch key political and trade agreements with the EU under pressure from Russia.
The rallies have since dwindled, but the opposition movement - led by three political leaders including former world boxing champion Vitali Klitschko - maintains a protest camp on Kiev's central Independence Square.
Several hundred protesters manning the camp were reinforcing the barricades Saturday.
"We are returning to Stalinism. When these laws are enforced the situation in Ukraine will be worse than in Russia or Belarus," Leonid Tertichny from the central Cherkasy region said at the protest camp.
"But these laws have not intimidated us, they mobilised people. The protests will continue."
Olena Oshchepovska said the new laws meant the government was afraid of its own people.
"The authorities are offering us to follow the path of Belarus but we will never agree to that," said the protester from the western city of Rivne.
In a fresh sign of tension within the administration, Yanukovych's office said late Friday his chief of staff, Sergiy Lyovochkin, was standing down and would instead act as an advisor.
Lyovochkin first submitted his resignation after riot police brutally broke up an opposition protest late last year but Yanukovych refused to let him go at the time.
Yanukovych's spokeswoman Darka Chepak may also leave, an official told AFP on condition of anonymity.
"Turmoil in regime in Kiev. Reports of resignations, dismissals and general uncertainty," Swedish Foreign Minister Carl Bildt said on Twitter.
"Regime likely to try to increase repression further."
Yanukovych signed the new laws despite requests from Western rights groups and senior officials to veto the bills, which they said were not in line with Ukraine's international commitments.
US Secretary of State John Kerry called the curbs anti-democratic and wrong, while EU foreign policy chief Catherine Ashton said she was "deeply concerned".
Ukraine's opposition fears the tough new laws will be used to break up the opposition movement and prosecute its leaders.
Provisions pushed through parliament on Thursday also introduced the term "foreign agent" to be applied to organisations that receive funding from foreign countries.
They also permit the arrest of protesters who wear masks or helmets, among other restrictions.
Jailed opposition leader Yulia Tymoshenko accused her arch-rival Yanukovych of seeking to establish a "neo-dictatorship", urging people to mount a strong response.
The protests in Ukraine - the largest demonstrations since the pro-democracy Orange Revolution in 2004 - have repeatedly descended into clashes with police in which hundreds have been hurt.