Eliminating the laws, which is likely to be done in a special parliament session Tuesday, would be a substantial concession to the opposition. But it does not meet all their demands, which include Yanukovych's resignation.
One of the opposition figures, Arseniy Yatsenyuk, turned down the prime minister's job, which Yanukovych offered him on Saturday.
At that time, he said protests would continue. In the Monday meeting, Yanukovych said a proposed amnesty for arrested protesters would not be offered unless demonstrators stopped occupying buildings and ended their round-the-clock protests and tent camp on Kiev's central square.
Protesters have been afraid that authorities were preparing to end the spreading demonstrations by force, but the foreign ministry said earlier the government has no immediate plans to declare a state of emergency.
Three protesters died in the clashes last week, two of whom were shot by hunting rifles, which police insist they do not use. With protesters now willing to risk injury, a state of emergency would be likely to set off substantial fighting on the streets of the capital.
"Today, such a measure is not on the table," Foreign Minister Leonid Kozhara told journalists.
EU foreign policy chief Catherine Ashton said in a statement that she was alarmed by reports about the government considering a state of emergency and warned that such a move "would trigger a further downward spiral for Ukraine which would benefit no one."
The protesters still occupy three sizable buildings in downtown Kiev, including City Hall. One of the buildings was seized in a spectacular assault early Sunday, when hundreds of protesters threw rocks and firebombs into the building where about 200 police were sheltering. The crowd eventually formed a corridor through which the police left.
Lukash, in a televised statement, noted that protesters seized the building as justice employees were working on measures to grant amnesty to protesters and to make changes in the constitution to restore more power to the prime minister.
It's not clear if constitutional changes will be on the agenda for Tuesday's parliamentary session, but granting more power to the prime minister could both sweeten the offer and allow Yanukovych to portray himself as offering genuine compromise.
The fears of a state of emergency come after other official statements suggesting the government is considering forceful moves against the protesters.
Interior Minister Vitali Zakharchenko, an official deeply despised by the protesters, on Saturday warned that demonstrators occupying buildings would be considered extremists and that force would be used against them if necessary. He also claimed demonstrators had seized two policemen and tortured them before letting them go, which the opposition denied.
The protests began in late November when Yanukovych shelved a long-awaited agreement to deepen ties with the 28-nation European Union and sought a bailout loan from Russia. The demonstrations grew in size and intensity after police violently dispersed two gatherings. Demonstrators then set up a large tent camp on Kiev's main square.
After Yanukovych approved the new anti-protest laws, demonstrations spread into other parts of the country, including to some cities in the Russian-speaking east, the base of Yanukovych's support.