Red-shirt spokesman Sean Boonpracong: "We demand they stop the killing"
Renegade Thai general Khattiya Sawasdipol, who was shot on Thursday as he backed protesters in Bangkok, has died, hospital officials have said.
The announcement came amid fresh fighting between the protesters and soldiers after Thai officials rejected a demand for UN-backed talks.
The government has called on protesters to leave the camp by 1500 (0800 GMT), saying the area is no longer safe.
Thirty-six people have been killed in the violence since Thursday.
Maj Gen Khattiya, known as Seh Daeng (Commander Red), was shot in the head on Thursday as he spoke to a New York Times journalist within the protesters' rally site.
He had been in a critical condition in hospital and had not been expected to pull through.
His shooting marked the beginning of clashes between soldiers and protesters that have raged on-and-off since then.
It is not clear who shot him, but some among the protesters were quick to blame army snipers.
A minute's silence was held for the general at the protesters' camp in the Ratchaprasong district, with some demonstrators in tears.
'A lot of shooting'
About 5,000 people remain in the encampment in Ratchaprasong, where food and water are running low amid a blockade on the area.
AT THE SCENE
Chris Hogg, BBC News, Bangkok
I can see about 200 metres down the Rama IV highway, but beyond that I cannot see anything because there is just thick black smoke coming from the tyres that have been set alight by the protesters.
Near to me are sandbag encampments behind which the Thai soldiers are standing. They have a policy of containment by fire in a bid to try and prevent people at the other end of the street from moving forward towards to them.
There are loud speakers sending out messages telling people it is no longer safe to be there and to leave as soon as possible.
In a television announcement, the government told protesters - particularly women, children and the elderly - to leave the camp by mid-afternoon, or face the prospect of two years in jail.
The protesters have been offered free transport home, but there are conflicting reports over whether they are taking up the government's offer of safe passage.
Hundreds of women and children have sought refuge in a nearby temple.
The fresh fighting overnight along a street of upmarket hotels saw the first death among the soldiers, officials said.
Guests at one of the hotels, the Dusit Thani, were rushed from their rooms into the building's basement after gunfire and explosions shook the area.
"Everybody was evacuated from their room and spent the night in the basement," a photographer for the Reuters news agency said. "There was a lot of shooting."
Besides the deaths, about 200 people have been injured in the clashes. Previous violence since the protests began in March has left more than 60 people dead and at least 1,600 wounded.
The Dusit Thani hotel is across from Lumpini Park in a district of expensive hotels, embassies and shopping malls that has been taken over by the protesters.
Army sharpshooters behind sand-bagged barricades have been firing live rounds at protesters.
Government spokesman Panitan Wattanayagorn said troops were "not using weapons to crack down on civilians". He said armed "terrorists" among the protesters were being targeted.
The protesters, called red-shirts after the colour they have adopted, have been throwing stones, petrol bombs and fireworks at the soldiers and setting barricades of tyres on fire.
There have been reports that some among them are armed.
The latest fighting broke out after the government rejected a call from a red-shirt leader, Nattawut Saikua, to hold UN-moderated talks to end the stand-off, providing the army withdrew from the area around the red-shirt camp.
Panitan Wattanayagorn insisted that no outside help was needed, and said on Monday the government would consider talks with the protesters if they are "sincere" about peace.
"The government is ready to go forward with negotiation when the situation is defused, when the protest ends, violence ends and attacks on authorities end," he said.
A state of emergency has now been declared in 22 provinces across the country - mostly in the protesters' northern heartlands - in a bid to stop more demonstrators heading to the capital.
14 Mar: Red-shirts converge on Bangkok, occupy government district
16 Mar: Protesters splash their own blood at Government House
30 Mar: Talks with government ends in deadlock
3 Apr: Occupy Bangkok shopping district
10 Apr: Troops try to clear protesters; 25 people are killed and hundreds injured
Protests have spread outside the capital with a military bus set afire in the northern city of Chiang Mai and demonstrations in two north-eastern towns in defiance of a government ban.
Prime Minister Abhisit Vejjajiva has declared Monday and Tuesday as public holidays and delayed the start of Bangkok's school term, but a planned curfew was cancelled.
He has already said the army will not back down in its operation to clear the protesters.
Many of the protesters are from poor rural areas in northern Thailand where support is still strong for former Prime Minister Thaksin Shinawatra, who was ousted in a 2006 coup.
He is living abroad to avoid a jail term on a corruption conviction.
The protesters say the current government is illegitimate, having come to power in a parliamentary vote after a pro-Thaksin government was forced to step down in December 2008 by a Constitutional Court ruling that it had committed electoral fraud.
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