Quebec Premier Jean Charest defended his government on Radio-Canada's talk show, Tout le monde en parle, on Sunday night. ((CBC))

Embattled Premier Jean Charest vowed to stay on the job and fix the corruption problems plaguing Quebec, he said on the province's most popular TV talk show on Sunday night.

As part of what people are calling a new charm offensive aimed at turning around a province appearing to lose faith in his leadership, Charest appeared on Radio-Canada's Tout le monde en parle, which attracts an average of 1.5 million viewers each week.

Charest made his pitch against a public inquiry into alleged corruption and influence peddling involving the construction industry, saying what the province really needs is to find the people responsible.

The ongoing investigation by a special anti-corruption squad will do a better job, he said, than a drawn-out public inquiry that could give immunity to those who testify.

"It takes proof," said Charest, in an exchange with Quebec actor Louis Morrissette.

"It’s not true that we are going to hang someone based on a headline in a newspaper."

'The national assembly is not a people's court. My job is not to follow the trends of the day. It's to make sure that Quebec does well.' — Jean Charest, Quebec premier

Charest's popularity has plummeted to 16 per cent according to recent polls, and an online petition calling for his resignation has collected more than 200,000 signatures since it was launched several weeks ago.

His party also lost a key byelection to the Parti-Québécois, in the riding of Kamouraska-Témiscouata, a seat formerly held by the late Claude Béchard.

The premier said he would not surrender, and told the audience that he has never been tired of fighting.

"The national assembly is not a people's court. My job is not to follow the trends of the day. It's to make sure that Quebec does well," said Charest.

Defamation case back in court

As Charest continues to try to restore public confidence in his administration, his defamation case against his former justice minister Marc Bellemare continues to make its way through the courts.

Charest is suing Bellemare for $700,000, alleging the former minister slandered the premier's reputation when he went public with accusations of peddling influence to nominate Liberal-friendly judges.

Bellmare has countersued.

The report from a public inquiry into Bellemare's allegations is expected to be released in the new year.