French president François Hollande took the biggest gamble of his two-year-old presidency on Monday by ordering his reformist prime minister to form a new government which will exclude Socialist dissidents demanding an end to economic austerity policies dictated by Germany.

Casting off his characteristic indecision, Hollande agreed to prime minister Manuel Valls's offer to dissolve the cabinet amid a political crisis triggered by the country's outspoken economy minister.

The dissolution of the cabinet allows Hollande to form a new government without dissenting voices.

In a defiant farewell speech at the economy ministry, Arnaud Montebourg, said the austerity drive in France and Europe was a "financial absurdity," and accused Hollande and Valls of ignoring his pleas for a "moderate and balanced" alternative.

Less than an hour after he was called into Valls's office for a 15-minute meeting, Montebourg said austerity-inspired tax increases had undermined purchasing power and has led to the rise of extremist parties.

Montebourg said the "incorrect" austerity policies followed by the European Central Bank and EU member states had "continued to mire the eurozone in recession and soon, deflation". Education minister Benoît Hamon and culture minister Aurélie Filippetti also said that they would not take part in the new government.

The departure of the three ministers will provide Valls, a social democrat, with the opportunity to reshape the government in his own image, said French political scientist Laurent Bouvet of the University of Versailles. "It will have the benefit of clarifying the situation for the first time," said Bouvet. If Hollande had allowed the sniping from the leftwing ministers to continue," he would have lost all credibility, in France and in Europe". But, he added: "The problem is, it's a big gamble."

Hollande, the most unpopular French president in living memory whose latest approval ratings stand at 17%, has been pilloried by the left for failing to make good on his election promise to restore growth. But his plans were opposed by German chancellor Angela Merkel who again last week rejected French and Italian appeals to soften eurozone deficit targets which they have failed to meet.

According to Bouvet, Hollande has only himself to blame. "He didn't make the tough economic choices when he had the opportunity after his election, he could have named Valls then. But he kept trying to please everyone, including in his own camp."

The French Socialist party has always been torn by opposing factions, but Bouvet said that at a time when the Socialists had electoral prospects the tensions between the different wings could be played down. Now, with the surge of the Front National amid a stagnating economy, the political landscape in France has changed drastically.

Montebourg, 51, has been a constant thorn in Hollande's side, who had shied from disciplining him despite his frequent off-message statements. As industrial recovery minister, he told the steel magnate Lakshmi Mittal in November 2012 that "we no longer want Mittal in France" amid high stakes negotiations aimed at keeping blast furnaces at Florange afloat.

But he sealed his own fate over the weekend, first in an interview with Le Monde, with a speech to a Socialist party rally on Sunday. "France is a free country which shouldn't be aligning itself with the obsessions of the German right," which were leading France down a "blind alley", he said.

He was joined in his criticism by Hamon. The third dissident minister, Filipetti, said in her resignation letter to Hollande and Valls that the crisis meant people had become disillusioned with politics and "in the worst case is throwing our voters into the arms of the Front National".

After aides to Valls let it be known on Sunday that Montebourg had crossed a "yellow line", the prime minister submitted the entire government's resignation on Monday ,after 147 days in office. Le Parisien reported that he had said to Hollande: "It's him or me," referring to Montebourg.

The president instructed Valls to form a new government "consistent with the direction set for the country". Valls has pledged to stick to a three-year plan in which deficits would be cut while the tax burden on businesses would be eased. The programme is to be financed by €50bn of spending cuts opposed by the left which wants tax cuts to boost consumer demand.

Valls spent the day in consultations and his new government is due to be announced on Tuesday. Analysts said that the cabinet would keep Hollande loyalists in key positions, including the finance minister Michel Sapin, agriculture minister Stéphane Le Foll and the defence minister Jean-Yves Le Drian.

The challenge for Valls is to put together a government that can win a confidence vote in the National Assembly, despite the revolt by the Socialist party's left flank, opposition from a breakaway party and desertion by the ecologists.

But Olivier Rozenberg, a specialist on parliamentary institutions with Sciences Po, said that Valls was likely to win the vote which could be held next week. "Although ideologically there may be a majority within the left which believes that the deficit cutting shouldn't happen, politically they are unlikely to vote against the government because that would mean the dissolution of parliament. And then then would lose their seats," he said.

With the party split now officialised with the three ministers leaving the government, the flamboyant Montebourg, who on Monday vowed to continue a "Made in France" campaign, appears as a potent flag-bearer of the left.

The crisis is unfolding as politicians are already eyeing the next presidential elections in 2017, with both Montebourg and Valls possible contenders. The prime minister has remained popular in the country as a whole although his approval ratings have shrunk by nine points in the last month. Hollande himself seemed strangely detached from the crisis as he stuck to his schedule attending commemorations marking the end of the second world war on Monday. He was shown on television drenched by pouring rain, making a speech on a remote Breton island, eight kilometres from the French mainland.