* Police say avoiding confrontation
* Protesters mingle with police at flashpoints
* Army says staying out of political issue (Recasts with police comment)
By Panarat Thepgumpanat
BANGKOK, Dec 3 (Reuters) - Thai police said on Tuesday they would not stand in the way of protesters battling to seize the prime minister's office and city police headquarters, focal points of demonstrations aimed at toppling the government of Prime Minister Yingluck Shinawatra.
A Reuters witness said police were clearing barbed-wire barricades from outside the police headquarters. Television pictures showed protesters and police officers mingling outside the building and Government House, where Yingluck's office is.
The protests have brought clouds of teargas, rubber bullets and intermittent gunfire to parts of Bangkok, the latest turmoil in the struggle between the Bangkok-based establishment and forces loyal to Yingluck and her brother, former Prime Minister Thaksin Shinawatra.
Protest leader Suthep Thaugsuban vilified the police in a speech to cheering supporters late on Monday and said the protesters would capture their city headquarters on Tuesday.
But, in a move to defuse the confrontation, city police chief Kamronvit Thoopkrachang said his men would not fight the protesters.
"In every area where there has been confrontation, we have now ordered all police to withdraw. It is government policy to avoid confrontation," Kamronvit told Reuters.
"Today, we won't use teargas, no confrontation, we will let them in if they want," he said.
Kamronvit is close to Thaksin, himself a former policeman and then a telecommunications tycoon, who became Thailand's most popular politician with policies to help the urban and rural poor.
A government spokesman was not immediately available for comment.
Yingluck had promised not to use force against the crowds trying to storm state agencies.
Early on Tuesday a helicopter dropped leaflets over the protesters reminding them that their leader, Suthep, was wanted on a charge of insurrection.
"So please, stay away from him and stay away from the unlawful gatherings," media quoted the government as saying in the leaflets.
Suthep is a former deputy prime minister of a government bitterly opposed to Thaksin that ordered the military to put down pro-Thaksin protests in 2010. About 90 people were killed.
Yingluck's government came to power with a landslide election victory in 2011.
More chaos and violence could have increased the chances of the army stepping in to restore order, but offering to let the protesters in to avoid bloodshed may make the government look magnanimous.
Thai financial markets have fallen sharply since the protests began more than a month ago but on Tuesday the baht was steadier at around 32.20 to the dollar, while the stock market rose 1 percent.
ARMY NEUTRAL, SO FAR
Thaksin was ousted by the military in a 2006 coup but while Yingluck said on Monday the army was staying neutral this time.
Army chief Prayuth Chan-ocha told reporters on Tuesday: "This is a political problem that needs to be solved by political means. However, we are monitoring from a distance."
Four people have been killed since the weekend and two protesters were shot and wounded on Monday, a hospital said, adding it was not known who shot them.
Thaksin's opponents hold considerable power and influence, among them wealthy conservatives, top generals, bureaucrats, royalists and many members of the urban middle class.
Many of them see Thaksin as a corrupt, crony capitalist who manipulates the masses with populist handouts and is a threat to the monarchy, which he denies.
He is adored by the urban and rural poor who would be outraged to see Yingluck's government removed. Yingluck said on Monday she was willing to explore every possibility for a peaceful solution. Her party would probably win any new election.
Suthep, 64, who resigned as a Democrat lawmaker to lead the protests, wants a vaguely defined "people's council" to replace the government.
Yingluck said that was unconstitutional. (Additional reporting by Apornrath Phoonphongphiphat and Kochakorn Boonlai; Writing by Robert Birsel; Editing by Alan Raybould and Raju Gopalakrishnan)