The Supreme Court issued arrest warrants for the couple after they fled to Britain saying that they could not get fair trials in Thailand in a number of cases involving alleged corruption and abuse of power.
Samak was earlier blasted by critics as a Thaksin puppet but appears recently to have steered an independent course, much to the chagrin of the toppled prime minister's followers who largely populate the PPP.
"I will not bow to the call from protesters and several other groups of people urging me to resign or dissolve the House," Samak said in his weekly television programme on Sunday.
"I will continue to look after this country as the prime minister."
Samak, whose party won national elections last December, has been under pressure from almost daily street protests by the anti-Thaksin People's Alliance for Democracy and himself faces several court cases involving alleged corruption, abuse of authority and conflict of interest.
On Saturday, his party members signed a letter saying Thaksin did not deserve to be treated like a criminal and that the circulation of the arrest warrant posters was "disturbing".
The group is to present the letter to Samak on Monday.
The posters appeared on front pages of almost all Thai newspapers on Saturday and were going up at every police station and immigration checkpoint in the country.
On Friday, the Supreme Court ruled that a corruption trial against Thaksin and his wife, Pojaman, could proceed even though the couple fled the country.
The malfeasance and conflict of interest charges stem from Pojaman's 2003 purchase of a plot of land in central Bangkok from a government agency when Thaksin was prime minister.
The Supreme Court has issued arrest warrants for the couple, and Thai prosecutors are discussing the possibility of asking for Thaksin's extradition - usually a lengthy and complicated process.
|Thai authorities issued arrest warrants after the couple fled to Britain [AFP]
On Sunday, the anti-Thaksin alliance urged the British government to repatriate the couple, and announced it would stage a rally in front of the British embassy in Bangkok on Tuesday to press their case.
Thailand has not yet asked Britain to extradite the former leader, who so far has not been granted asylum or special treatment in Britain, where he owns several expensive properties and the Manchester City football club.
Thaksin returned to Thailand less than six months ago after an extended period of exile following a coup in September 2006 ousted him.
Thaksin, 59, faces several court cases but has repeatedly claimed he is innocent of all charges.
On July 31, the criminal court convicted his wife of evading millions of dollars in taxes and sentenced her to three years in prison.
She was out on bail pending an appeal when she and her husband, on a trip to Beijing to attend the Olympics, decided to return to exile in Britain.