Kerry, speaking with German Foreign Minister Frank-Walter Steinmeier during a visit to Berlin, also said "outside powers" should not get involved in a crisis that he said was for the Ukrainian people to resolve.
"The offers of President Yanukovich have not yet reached a level that would be sufficient regarding the reforms," Kerry said, according to a German translation of his remarks.
Yanukovich has accepted the resignation of his government and offered amnesty from prosecution for peaceful protesters, in a gesture to demonstrators camped out in Kiev. However, they and the main opposition leaders are pressing on with their protests.
Yanukovich, who looks increasingly isolated in a tug-of-war between the West and Ukraine's former Soviet overlord Russia, suddenly withdrew from view on Thursday, complaining of a high temperature and acute respiratory ailment.
A presidential spokesman, contacted by Reuters on Friday, had no update on the president's condition. Nor could he say when he might be back at his desk.
At least six people have been killed and hundreds more injured in street battles between anti-government demonstrators and police, which have escalated sharply in recent weeks after the authorities toughened their response.
The currency hryvnia slumped 2.5 percent against the dollar on Friday for its biggest one-day fall since the third quarter of 2009. Analysts attributed the drop to political developments and fears Russia may halt the disbursement of its $15 billion loan package that saved Ukraine from the brink of default later last year.
RADICAL GROUP MAKES THREATS
A radical Ukrainian nationalist group called Right Sector, seen as being behind violent clashes with police in Kiev, meanwhile demanded the release of activists detained by police, threatening to take the law into their own hands to free their comrades.
"If they (police) refuse, appropriate steps will be to taken to free these people and not only constitutional methods will be used," Right Sector leader Dmytro Yarosh told reporters.
Right Sector, a paramilitary group whose violent actions have appalled opposition leaders and peaceful protesters, also said it wanted to play a direct role in any negotiations for a settlement between Yanukovich and opposition leaders, he said.
An anti-government activist who vanished a week ago appeared on television on Friday, his face badly beaten and with wounds to his hands, saying he was kidnapped and tortured by his abductors who had "crucified" him.
Dmytro Bulatov, 35, who was one of the leaders of anti-government protest motorcades called 'Automaidan', was taken to hospital after he appeared on Ukrainian television.
"They crucified me. They punctured my hands," he said, pointing to marks on the backs of his hands. "They cut off my ear, slashed my face," he said. "But I am alive, thank God."
The United Nations' human rights office called for an investigation into reports of kidnappings and torture, and European Union foreign policy chief Catherine Ashton said she was appalled by the signs of torture inflicted on Bulatov.
"All such acts are unacceptable and must immediately be stopped," she said in a statement. "It is the authorities' responsibility to take all necessary measures to address the current atmosphere of intimidation and impunity which allows for such acts to take place."