The amnesty law only takes effect if protesters end building occupations in the capital, Kiev, and some other western cities, the Wall Street Journal reported.
The latest round of mass demonstrations, building occupations and arrests began when Yanukovych abruptly abandoned plans to enter a European Union cooperation agreement. Russia has been pressuring Ukraine to turn away from the EU.
Yanukovich approved new restrictions on demonstrations in January.
The president and his opponents traded accusations that each side was trying to scuttle efforts to end the country's political crisis.
Yanukovych left the negotiating table Thursday, taking sick leave because of a fever and a respiratory ailment. An aide said Yanukovych remained in control but a statement issued by his office didn't indicate when the 63-year-old Yanukovych would return to work.
Opponents accused him of using sickness as a delaying tactic.
"The president's sickness is a political disease," opposition party leader Vitali Klitschko, said in a statement. "This is a withdrawal from [the] political crisis" to give him a respite from "urgent decisions."
Protests began in November after Yanukovych nixed a long-planned trade and political agreement with the European Union. He later signed an agreement with Russia that included a $15 billion aid package.
After a violent police crackdown, protests expanded into a broader outcry against police violence and government corruption. Ukrainian Prime Minister Mykola Azarov resigned this week, triggering the resignation of Yanukovych's Cabinet, although it will remain in place until a new government is formed.
Russia is reported to be holding back some of the $15 billion package it offered Ukraine last year, saying it needs to understand the composition of Yanukovych's new Cabinet.
In a post on his website, Yanukovych signaled he won't make any more concessions.
"Authorities fulfilled all obligations that they took upon themselves," he said, adding that protesters may be trying to use the situation to their advantage.
An anti-government protester who disappeared a week ago was found bloody, bruised and missing part of an ear in a village near the Ukrainian capital, supporters said.
Dmytro Bulatov, 35, one of the more visible figures opposing Yanukovych's government, said he had been tortured, including having nails pounded through his hands, the Wall Street Journal reported.
Supporters said Bulatov was found Thursday wandering in the unnamed village.
"There's not a single healthy part of my body, as you can see. But I'm alive, thank God," Bulatov told reporters before going to a hospital.
Opposition leaders noted two other activists were kidnapped and tortured this month. The body of 50-year-old Yuriy Verbystskiy was found frozen to death Jan. 22 along the side of a road outside Kiev after a beating left him unable to walk to safety. Another activist who disappeared at the same time was found was badly beaten, but survived.
Authorities deny involvement in the kidnappings, which they said were being investigated. They had no immediate comment about Bulatov's description of his abduction, the Journal said.
European Union and U.S. officials have expressed concern about the disappearances.
"These disappearances are completely at odds with human values and have no place in a modern, democratic society," U.S. Ambassador Geoffrey Pyatt said Thursday.