In response, Nattawut Saikua, a leading red shirt, said that they would not continue talks with the govenrment.
"These negotiations will stop. We will not talk anymore," he said.
The red shirts' offer had been eased from an earlier demand that snap polls be held.
At least 26 people have died and hundreds have been injured during the weeks of protests.
There have been clashes between police and protesters and on Thursday five grenades were thrown in Bangkok's central business district near non-alligned anti-red shirt protesters, killing one person.
The red shirts denied that they were behind the grenade attacks.
Many of the red shirts support Thaksin Shinawatra, the former prime minister ousted in a 2006 coup, and the group have been occupying Bangkok's main upmarket shopping area in Rachaprasong for three weeks.
Abhisit's government has so far refused to disperse them as it risks heavy casualties and the prospect of clashes spilling into high-end residential areas.
Increasing anger has been felt among government supporters and also Bangkok residents, who are upset this protest is going on in their city.
The red shirts, formally known as the United Front for Democracy against Dictatorship, want the prime minister to step down, dissolve parliament and call new elections.
But Abhisit has rejected claims that his government is illegitimate and has refused to give up his post.
The central bank said on Wednesday that the political crisis was affecting confidence, tourism, private consumption and investment, although exports, which are crucial to economic growth, have been little affected by the unrest.