Ukraine's President Viktor Yanukovich has offered a conditional amnesty to jailed opposition activists and repealed controversial anti-protest laws in an attempt to calm two months of political chaos and civil unrest.
The measures, announced on Friday by his office, give protesters a 15-day deadline to leave the public buildings they have occupied.
The latest concessions from Yanukovich came as the police said they had launched an investigation into the abduction and alleged torture of an opposition activist, Dmytro Bulatov.
We are appalled by the deaths reported in recent days in Kiev, which should be promptly, thoroughly and independently investigated
Oleg Tatarov, Ukraine's deputy chief investigator, said at a briefing that Bulatov's friends took him for medical treatment instead of calling police to the scene right away.
An arrest warrant has now been issued against Bulatov.
Bulatov, a 35-year-old activist from the Avtomaidan group that organised protests against Yanukovich, stumbled into a village outside Kiev more than a week after his wife first reported him missing.
Bulatov appeared on television on Friday, his face badly beaten and with wounds to his hands, saying his abductors had "crucified" him.
Bulatov's account drew immediate international condemnation, with the UN's human rights office calling on Ukraine to launch an independent probe into deaths, kidnappings and torture amid the raging political unrest.
"We are appalled by the deaths reported in recent days in Kiev, which should be promptly, thoroughly and independently investigated," said Rupert Colville, spokesman for the UN High Commissioner for Human Rights.
"We are also calling for an investigation into reports of kidnappings and torture."
Catherine Ashton, EU foreign policy chief, warned Ukrainian authorities that targeting activists "must immediately be stopped".
Amnesty International said the "barbaric act" must be investigated, adding that it is only one of several cases of similar disappearances.
The US embassy in Kiev posted a picture of Bulatov with a blackened gash on his cheek and said that "the government of Ukraine must take full responsibility for the timely investigation, capture, and prosecution of those responsible for this heinous crime".
It further voiced concern over reports of 27 more missing activists, in a statement posted on its official Facebook page.
Vitaly Klitschko, UDAR (Punch) opposition party leader and former boxing champion, said Bulatov was tortured "to scare those who disagree with the regime, to show that it can happen to anyone".
In a video of Bulatov made by fellow activist Oleksiy Grytsenko, he said that despite the atrocious torture, he would keep protesting. "They won't scare us," he said.
The amnesty law was backed by Yanukovich's Regions Party, but some opposition politicians said the new law would mean the jailed protesters were effectively being held hostage until the buildings were vacated.
John Kerry, US secretary of state, said the Ukranian president's offers needed to improve if the opposition were to take them seriously.
At least six protesters have died and hundreds more have been injured in the latest round of protests which began in November last year.
Under the amnesty law, protesters will have to vacate Grushevsky Street in the capital Kiev, where several activists have been shot dead during clashes with security forces.
They will also have to leave streets and squares they have been occupying "except those where peaceful protest actions are taking place".
This opens the possibility that protesters could be allowed to stay at their tented city in Kiev's Independence Square.
Yanukovich, who on Thursday went on indefinite sick leave, also signed legislation scrapping anti-protest laws passed earlier this month that ignited the two-month protest movement.
The Ukrainian armed forces weighed in on the crisis for the first time, calling for Yanukovich to act urgently to stabilise the situation.