"The Americans asked us to negotiate directly with them in Montreux," Syrian Foreign Minister Walid Muallem told Syrian state media on the plane home from 10 days of peace talks in the Swiss cities of Montreux and Geneva.
"But we refused to do so before Secretary of State John Kerry apologised for what he said at the conference," Muallem added, in remarks carried by state news agency SANA.
State Department spokeswoman Jen Psaki denied there was any attempt at direct negotiations.
"At no point did the United States offer to negotiate directly with the Syrian regime and at no point will Secretary Kerry ever apologize for speaking the truth about the brutality the Assad regime has inflicted on the people of Syria," Psaki said.
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"There is no way, not possible in the imagination, that the man who has led the brutal response to his own people could regain legitimacy to govern," Kerry said.
During 10 days of talks the regime and opposition made no progress on ceasefires, humanitarian corridors or the question of a transitional government.
The regime sought to focus the discussions on "terrorism", its term for the actions of all those seeking Assad's overthrow.
A second round of talks has been tabled for February 10, with the opposition already committed to attending.
More than 136,000 people have been killed in Syria since the beginning of the conflict in March 2011, according to the Syrian Observatory for Human Rights, and more than 2.4 million Syrians have become refugees.