KIEV, Ukraine — Ukraine’s beleaguered president on Monday agreed to scrap harsh anti-protest laws that set off a wave of clashes between protesters and police over the past week, a potentially substantial concession to the opposition that stopped short of meeting all of its demands.

In a possibly major sticking point, 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 Independence Square, according to a statement by Justice Minister Elena Lukash on the presidential website.

President Viktor Yanukovych has been under increasing pressure since he pushed the tough laws through parliament, setting of clashes and protests in other parts of the country in a sharp escalation of tensions after weeks of mostly peaceful protests over his rejection of a deal to deepen ties with the 28-nation European Union.

At a meeting between top opposition figures and Yanukovych late Monday “a political decision was made on scrapping the laws of Jan. 16, which aroused much discussion,” Lukash said.

She made no mention of a key opposition demand – that Yanukovych resign.

One of the opposition figures, Arseniy Yatsenyuk, turned down the prime minister’s job, which Yanukovych had offered Saturday, the statement said.

Eliminating the laws, which is likely to be done in a special parliament session Tuesday, appears to be a serious step back for the government. The session is also expected to include a discussion of government responsibility in the crisis, suggesting a Cabinet reshuffle could be imminent.

On Independence Square, there was no immediate reaction from the relatively small crowd gathered in bitter cold near midnight.

A key issue will be the amnesty offer, which could allow for the release of dozens of protesters being held in jail in exchange for an end to the demonstrations.

The statement did not say the opposition would agree to those terms. Doing so could infuriate radical factions within the broad-based protest movement, such as the group called Right Sector that has driven much of the recent violence.

Several hours before the statement, Right Sector issued its own demands, which include punishing officials responsible for the deaths and abuse of protesters, disbanding Ukraine’s feared riot police and locating all missing opposition figures.