He said some sort of response would be made on Tuesday, adding that he thought Veera Musikapong, the UDD chairman, would probably seek talks with the government on Abhisit's plan.
Abhisit said he would proceed with his plan even if the red shirts rejected it, but in that case he would not set a date for the election.
Thaksin Shinawatra, the former prime minister ousted in a 2006 military coup and now exiled, called on his supporters, whom many people link to the red shirts, to seek "reconciliation" following the offer.
Al Jazeera's Wayne Hay, reporting from Bangkok, said the prime minister had said this was the last chance for the red shirts to reach an agreement, and had set Tuesday as a firm deadline for the protest leaders to respond.
In the meantime, our correspondent said, the military and government were preparing for a possible crackdown to clear out the protesters, preparing armoured personnel carriers to enter the protest site, where thousands of red shirts remained on Tuesday.
Pressure has been building on the red shirts to end their two-month protests which have triggered clashes with government forces that have claimed 27 lives and left about 1,000 injured.
Businesses in the capital's main commercial area and the crucial tourism sector have been badly affected and a red-shirts raid on a nearby hospital last week looking for soldiers was roundly criticised.
Roberto Herrera-Lim, an analyst at risk consultancy Eurasia Group, said "the game plan is for the government to make it appear this offer is reasonable".
"If the red shirts reject it, they'll be seen as the unreasonable party and that will then give the government a chance to go after them," he said.
But, our correspondent said, 24 red shirt leaders still face arrest - some for criminal offences - and one of their conditions is amnesty for those involved in the protests.
Requesting for amnesty
Abhisit has said he is willing to consider amnesty for those who violated emergency regulations, but not for those who committed criminal offences.
The prime minister is also under intense pressure to end the political stalemate that has prompted the International Crisis Group to warn Thailand could slide into an "undeclared civil war".
"It doesn't seem like much of a compromise. Judging by the goals of the red shirts, I don't think they'll go along with this [conditions]"
Roberto Herrera-Lim, risk analyst, Eurasia Group
He rejected an offer last month by the red shirts to end their downtown siege in return for elections within three months.
He also previously offered an election in December, about a year before his term ends, and some analysts were sceptical that the slightly earlier date offered on Monday would satisfy the red shirts, who broadly back Thaksin.
They say both sides want to be in power in September for two critical events: a reshuffle of leaders in the military and police force, and the passing of the national budget.
"It doesn't seem like much of a compromise," Herrera-Lim said. "This just shows how crucial the timeframe is and the importance of having that reshuffle of the military and police take place before an election.
"Judging by the goals of the red shirts, I don't think they'll go along with this."
In his televised statement on Monday, Abhisit set five broad conditions for reconciliation.
The monarchy, he said, should not be dragged into politics or "violated" - a condition that follows government accusations some red shirts aim to overthrow the monarchy.
|Thai security forces are on standby to clear out protesters from central Bangkok [AFP]
The second condition calls for reforms to address social injustice, the third proposes an independent body to monitor media to ensure unbiased reporting, and the fourth a committee to investigate recent political violence.
The fifth point broaches possible political reforms that could include constitutional amendments and a review of a five-year ban on politicians allied with Thaksin.
Thanet Charoenmuang, a political science professor at Chiang Mai university, said "no one is going to disagree with the five conditions; they are just decoration because that's the language you use in any call for national reconciliation".
"But the point is that this is the first concrete offer from the government," he said.
"The ball is now in the red shirts' court to see if they want something they can hold on to, get their victory and go home, or keep pushing forward into an uncertain future."