Bettencourt's lawyer could not be immediately reached for comment.
Sarkozy said Woerth was a victim of calumny "without the slightest reality" and he wished people would take more interest in big issues such as health care and pensions rather than in "those who create scandals".
In an emotional live television interview, Woerth denied the allegations and said he was victim of a "cabal" by the Socialist opposition, insisting he would not resign because he was innocent and the real target was Sarkozy.
"I never, never received a single illegal euro," the centre-right minister and treasurer of the ruling UMP party said, his voice quivering with anger.
"Everything is false. It's defamation. I am the minister who fought hardest against tax evasion. The Swiss resent me to death," he said, referring to his previous role as budget minister.
French law limits donations to parties to $9,400 per person per year. Only $190 may be given in cash.
Earlier on Tuesday, Socialist and Communist members walked out of parliament after a centre-right minister accused the opposition of "playing the game of the extreme right" by asking repeatedly about the allegations during a question-and-answer session.
"These accusations are completely unacceptable," Jean-Marc Ayrault, a Socialist politician, said.
"When we ask for explanations, for clarification from the government, we are accused of playing the game of the extreme right."
Woerth is leading a major pensions reform and is a key ally of the president, whose approval rating hit an all-time low of 26 per cent last week amid sleaze allegations involving several ministers.
Thibout said she had not handed the money to Woerth personally but had given it to Bettencourt's financial consultant, who had told her he would make the handover.
|Woerth, right, denied the allegations and said the real target was Sarkozy [EPA]
Woerth's wife worked for the consultant until last month.
Woerth has already denied any conflict of interest between his roles as party treasurer and budget minister until March.
Patrice de Maistre, the consultant, was questioned by police on Tuesday and flatly denied Thibout's version of events, a spokesman for the Nanterre public prosecutor said.
Leading members of Sarkozy's party urged the president to bring forward a reshuffle planned for October and broadcast to the nation before he goes on his summer holiday on July 14.
Two junior ministers resigned on Sunday after being accused of wasting taxpayers' money on cigars and a private jet.
"The president says he is in control of the timing, but Woerth is more and more under fire. It's becoming politically difficult," UMP politician Jacques Myard told the Reuters news agency.
Marie-Anne Montchamp, another UMP parliamentarian, said: "We are stuck in a crisis. There needs to be a reshuffle, and fast."
Mediapart broke the news last month of secret recordings of conversations between Bettencourt and her financial consultant.
The website quoted Thibout as saying Sarkozy had been one of several politicians who regularly received envelopes of cash directly from the billionairess and her late husband, Andre, while Sarkozy was mayor of the Paris suburb of Neuilly in the 1980s and 90s.
Asked about this allegation, an official in Sarkozy's office said: "That's totally false."