The sex scandal surrounding France's culture minister has come at a bad time for President Nicolas Sarkozy whose popularity among voters took another dip, according to a poll published Friday.

The survey was conducted this week, when Culture Minister Frederic Mitterrand had to defend his honor over a book he wrote describing paying young men for sex.

Mitterrand has kept his job so far, but the controversy has posed yet another challenge for Sarkozy, who is struggling with France's worst economic slump since World War II.

Sarkozy hasn't spoken publicly about Mitterrand's book, though Mitterrand said the two met privately Thursday and Sarkozy "confirmed his confidence" in the culture minister.

The poll by the CSA agency shows 41 percent of respondents trust the president to confront the country's problems, down 6 percent from a month earlier. The poll of 1,003 people was conducted by telephone Tuesday and Wednesday. No margin of error was given.

The polling agency noted a particular drop in support among Sarkozy's core voters, who oppose his policies of reaching out to those outside his right-wing circle — such as Mitterrand, nephew of the late former French president, Socialist Francois Mitterrand.

Politicians and voters remained divided over the culture minister, after he went on national television Thursday night to tamp down calls for his resignation and explain his complicated personal past.

Mitterrand is an easy target for traditionalists: Openly gay, he wrote a book in 2005 called "La mauvaise vie," or "The Bad Life," in which he details encounters with male prostitutes in Thailand.

He uses the ambiguous term "boys," common language in French to refer to gay men. Mitterrand recently jumped to the defense of filmmaker Roman Polanski, in a Swiss jail on U.S. charges related to sexual relations with a 13-year-old girl.

Calls from the extreme right and the left mounted this week for Mitterrand's resignation.

Speaking on TF1 television Thursday, he insisted he had not hired minors and that the book was not a straight autobiography. He said he had no intention of quitting his job.

"I condemn sexual tourism, which is a disgrace. I condemn pedophilia, which I have never in any way participated in," Mitterrand said. "All those who accuse me of this kind of thing should be ashamed."

Some in the governing UMP party welcomed his explanation.

"I found him very moving," Justice Minister Michele Alliot-Marie said Friday on BFM television. "In each person's life, there are doubtlessly difficult periods, and shadows."

Mitterrand's staunchest critics were unconvinced. Marine Le Pen, vice president of the far-right National Front party, called him a "liar" and reiterated calls for him to be fired. She ignited the controversy this week by reading excerpts from the book on television.

While politicians' personal lives in France are traditionally considered private business, Mitterrand's experiences have worried some.

"He should resign. What he did is serious, not OK and not legal. He shouldn't be in the government anymore," said Alexandre Binon, a 24-year-old student from Rouen visiting Paris.

The book raised no more than literary eyebrows when it was published, and it drew little attention when Mitterrand was named to the government in June. Until he became France's guardian of culture, Mitterrand was known primarily as a television personality who made profiles of the famous.