"I'm not instigating it, I keep telling them we should do it peacefully, each day I tell them peaceful, peaceful, peaceful," he said.
Thaksin was ousted as prime minister during a bloodless coup in 2006 and was convicted in absentia of violating a conflict of interest law.
He is also accused in Tuesday's warrant of inciting people to break the law and cause unrest, a charge punishable by seven years in prison.
Thaksin said he would only return to Thailand to face trial if a "neutral body' had carried out the investigation and he could be guaranteed a fair trial.
Early on Tuesday, up to 2,000 protesters who have been camped around Government House for more than two weeks were encircled by soldiers, raising fears of a repeat of Monday's bloody clashes.
But after a meeting of representatives of both sides, protest leaders called on the demonstrators to abandon their positions and they began to move away with their arms raised.
As the protesters began to file away, a protest organiser told Al Jazeera they were not giving up their fight to force the Abhisit Vehjjajiva, the Thai prime minister, from power.
"There is no loss, we're taking a step back in order to go forward," Suporn Atthawong said.
"We’ll be back at a later date.
"We have decided to call off the rally today because many brothers and sisters have been hurt and killed. We don't want everybody to suffer the same. And we will not allow more deaths."
At least two people were reported killed overnight, apparently in clashes with pro-government supporters.
More than 120 people are reported to have been injured.
Abhisit said the military had used "soft means" in handling the protests and welcomed the decision to halt the demonstrations.
"I don't consider this a victory or defeat, but it's a victory for peace in society," he said in a televised speech.
"The operation under the state of emergency is not over. There are still things to do. I insist the government will not be negligent because we have to remain vigilant."
Political tensions have simmered since 2006 when Thaksin was ousted by a military coup amid accusations of corruption and abuse of power, a year after he won re-election in a landslide.
|Abhisit praised what he said was the 'soft means' used by the military [Reuters]
He remains popular among Thailand's rural poor for the populist policies he introduced.
Despite being in self-imposed exile, Thaksin remains an influential force and has sent almost daily video and audio messages to Red Shirt rallies, supporting their call for the current prime minister to resign and hold fresh elections.
However, Thaksin told Al Jazeera on Tuesday that he did not aim to become prime minister again.
"I'm not really wanting to be prime minister, but if the country needs me, if the people need me I will. Because I'm 60 in July I want to spend my life peacefully," he said.
The Red Shirts took their cue from protests last year by rival "Yellow Shirts" who took to the streets in huge demonstrations against successive pro-Thaksin governments.
Those protests culminated in the shutdown of Bangkok's two airports and court rulings ordering the dissolution of the government, paving the way for Abhisit to take power in December.
The Red Shirts took to the streets last month, accusing Abhisit of taking power illegally.
They say the Thai elite – the military, judiciary and other unelected officials – are interfering in politics, and are seeking Thaksin's rehabilitation.