Ukraine's embattled president has offered to make a top opposition leader the prime minister.
It is unclear though if the overture will mollify the radical faction of protesters who have clashed with police for much of the last week.
The offer by President Viktor Yanukovych 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 Kyiv when Yanukovych shelved a long-awaited trade pact with the EU in favour 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.
As former foreign minister, Arseniy Yatsenyuk 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 of the 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, the centre of the protests, later Saturday. In the meantime, opinions on what they should do were sharply divided.
"Blood has already been spilled; now we need to stop the country from breaking up," said Alina Semenyuk, a demonstrator on the square, known in Ukrainian as the Maidan, which has also become a term encompassing the entire protester movement.
But a few hundred meters away, on a street where police and demonstrators have clashed for a week, Artem Khilkevich declared "the authorities blinked and are trying to buy us. The Maidan is not for sale."
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. The opposition denied any such seizure and claimed Interior Minister Vitali Zakharchenko was making a bogus claim in order to justify a police sweep against protesters.
Three protesters have died in the past week's clashes, two of them from gunshot wounds. The Interior Ministry said a policeman was found shot in the head overnight. No arrests have been made or suspects named.
Protesters have rained stones and firebombs on police while officers retaliate with stun grenades and tear gas. On Saturday night, flames leapt high from barricade of burning tires, but there was no obvious violence in the Maidan. Demonstrators milled about, many of them holding clubs, metal rods and large sticks.
Yanukovych also agreed to discuss ways of changing Ukraine's constitution toward a parliamentary-presidential republic, which was one of the demands of the opposition.
If that change went through, the prime minister would have more powers and would be elected by parliament, not appointed by the president. Yanukovych backers currently have a majority in the parliament and the next election for the legislature is to be in 2017.
In Lviv, where support for Yanukovych is minuscule, regional lawmakers voted Saturday to establish a parallel government. Although the move was largely symbolic, it demonstrated the strong animosity toward the government in Ukraine's west. Ukrainian politics largely is divided between the Russian-speaking east, which is the industrial heartland, and the Ukrainian-speaking west.