KIEV, Ukraine — Ukraine’s embattled president on Saturday offered to make a top opposition leader the prime minister, but it was unclear if the overture would mollify the radical faction of protesters who have clashed with police for much of the last week.

The offer by President Viktor Yanukovych to make Arseniy Yatsenyuk the premier could be seen as either a concession to the opposition or as a strategy to put it in a bind, caught between a compromise-seeking European Union and angry protesters who don’t want to back down.

The protests began in November in Kiev when Yanukovych shelved a long-awaited trade pact with the EU in favor of closer ties with Russia, and boiled over into violence a week ago over harsh new anti-protest laws that Yanukovych pushed through parliament. Protesters have seized government buildings in scores of other cities in the European-leaning western part of the country.

Yatsenyuk, as a former foreign minister, led efforts to bring Ukraine into closer integration with the EU. Western countries have called on the adversaries to seek compromise, and rejecting Yanukovych’s offer could open Yatsenyuk to criticism.

But accepting the post would be seen by many protesters as capitulation and a betrayal of the movement’s ideals, especially after three demonstrators were killed in clashes this week.

Yatsenyuk and fellow opposition leader Vitali Klitschko, who was offered a deputy premiership, were to speak to the crowd on Independence Square later Saturday.

The offer came hours after the head of the country’s police, widely despised by the opposition, claimed protesters had seized and tortured two policemen before releasing them.