The French president, François Hollande, has insisted he did not cover for his disgraced former budget minister Jérôme Cahuzac, whose shock confession to having hidden €600,000 from the taxman in a secret foreign bank account has plunged the government into crisis.

In an attempt to lessen the impact of a scandal threatening to derail his government, Hollande made a surprise TV address on Wednesday following Cahuzac's spectacular admission that, despite four months of vowing on TV and in parliament that he had no foreign bank account, he had in fact hidden money abroad for around 20 years. Cahuzac, who until last month was Hollande's tax tsar and budget minister in charge of a crackdown on tax evasion, now faces charges for laundering money from tax fraud.

Hollande said Cahuzac did not benefit from any protection from the government. Shaking his fist, he called Cahuzac's actions unforgivable and "an outrage to the republic". He announced a string of reforms, including banning convicted fraudsters from holding public office and requiring all government ministers and members of parliament to publish details of their personal finances.

But opposition politicians demanded a parliamentary inquiry and criticised Hollande for standing by Cahuzac for four months after the investigative website Mediapart broke the story of the bank account in December. Cahuzac only resigned two weeks ago, in order to "defend his honour", when the French justice system stepped up its inquiry into the alleged account.

Jean-Francois Copé, head of the rightwing UMP party, said the president either "knew nothing, and that's extremely serious because it means he showed a certain amount of naivety" or "he knew and that means he lied to the French people". Thierry Mariani, UMP's vice-president, said of the Socialist leadership: "Frankly I find it hard to believe that they only learned the truth 48 hours ago, or else I guess we're being led by a big simpleton."

At parliamentary questions, MPs piled pressure on to the finance minister, Pierre Moscovici, accusing him of using his ministry's administration to try to clear Cahuzac's name before the legal inquiry had run its course. The UMP MP Claude Goasguen said Moscovici should resign, but Moscovici said: "If you're looking to accuse someone, you're knocking on the wrong door." He told Le Monde of Cahuzac: "Every time, and it was more than 50 times, when I interrogated him, he gave me numerous and vigorous denials, looking straight into my eyes." Moscovici said his only mistake had been showing "too much trust".

As opposition politicians wondered how the Élysée could not have established the truth of the account months ago, the interior ministry issued a statement saying there was no "parallel inquiry" or involvement of the secret services. The prime minister insisted that unlike previous administrations, the Socialist government was letting the justice system take its course and not pressuring investigators.

Cahuzac, 60, was a cardiologist who later made a fortune in plastic surgery by setting up a hair-transplant clinic near the Champs-Élysées. He famously spruced up the balding pates of some of France's most high-profile men for substantial fees. "When you can't see the join, it means he did it," one Socialist MP told Le Nouvel Observateur of Cahuzac's trichological expertise. Elected MP in 1997, he headed the parliament's commission on public finances. As Hollande's budget minister, his entourage called him the star of government.

The French media continued to question where the money in the secret foreign accounts had come from. In the late 1980s, Cahuzac worked in the health ministry, in charge of dealing with the powerful French pharmaceutical industry. At the time, he flatly denied any question of payments from pharmaceutical companies. Cahuzac's lawyer, Jean Veil, said the money in the foreign account, which had not been topped up for 12 years, came from "his income as a surgeon" and "his activity as a consultant". After leaving the health ministry, Cahuzac set up a consultancy firm working with pharmaceutical groups.

The intrigue surrounding the account deepened when Le Monde reported that the Swiss bank account set up by Cahuzac in 1992, before being transferred to Singapore, was opened for him by a former lawyer who had been a member of a far-right students' union and who was close to the leader of the far-right Front National, Marine Le Pen.

Swiss prosecutors confirmed that Cahuzac had agreed to allow details of the Swiss account to be transferred to French investigators.