"The election should be postponed on condition that the protesters cease their rallies and there is no blockade or boycott of the election," said Varathep Rattanakorn, an official from caretaker premier Yingluck Shinawatra's office.
"If there are still attempts to interrupt the election, there is no use in postponing it."
Yingluck had been informed of a decision by the Constitutional Court yesterday, which unanimously ruled that the snap polls can be postponed, Varathep said.
But the protesters rejected the terms set by the government for postponing the polls.
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"This isn't about compromise," protest leader Suthep Thaugsuban said. "The people will never go home because what the people want is political and national reform."
In a key development, Election Commissioner Theerawat Theerarojwit said the poll panel believes the vote should be postponed.
"As for the February 2 election, I don't believe it can be held," he told reporters. "It won't be able to be held because if there are elections on that day people could get hurt, and the (Elections Commission) doesn't want people to get hurt."
The debate over postponing snap polls comes as the country prepared for advance voting on Sunday which the protesters said they would block.
A section of voting will take place tomorrow in some places ahead of February 2 polls.
About 2.16 million of the total 49 million eligible voters have applied for advanced voting.
The protesters, who launched their anti-government campaign in November, have been demanding that Yingluck should step down and make way for an unelected "People's Council" to carry reforms before any polls.