Interviewed in the conservative Le Figaro, Mr Chirac, 60, the most likely conservative candidate for the next presidential elections due in 1995, said 'cohabitation' with the Socialist President, did not mean 'sharing power with an expiring socialism, it is the full exercise of responsibility by the new majority'.
Sources at the Elysee Palace then dropped hints to the French media that statements by the leader of the Gaullist RPR had irritated Mr Mitterrand, 76, and could prompt him to choose a prime minister from the centre-right Union for French Democracy (UDF), the Gaullists' partner, after the second round of National Assembly elections on Sunday.
This followed the last cabinet meeting of the Socialist government on Wednesday when, according to French newspapers, Mr Mitterrand predicted a series of crises under the right, including violence in the poor, immigrant-populated suburbs.
'When the suburbs go up in flames, you will see riot police hitting young people,' he was reported to have said.
'Those who laughed at me when I spoke of defending social rights will realise they exist when the right starts to attack them.'
Such comments are a foretaste of the dissident-in-chief role that the conservatives fear Mr Mitterrand will affect as long as he remains in office.
The first round of the elections last Sunday gave 40 per cent of the vote to the conservative alliance which looks set to take 450 or more of the 577 assembly seats, the biggest government majority of the 35-year-old Fifth Republic.
The humiliation of the ruling Socialists, 12 years after Mr Mitterrand was first elected to the presidency, was a personal blow for the head of state.
With victory in sight, some of the division between the RPR and the UDF, reflecting a longstanding feud between Mr Chirac and Valery Giscard d'Estaing, the former state president and founder of the UDF, re-surfaced. Mr Chirac said on Tuesday that Mr Mitterrand should accept the consequences of the 19 per cent vote for the Socialists and step down.
Mr Giscard d'Estaing responded by saying that the new majority should have made it clear beforehand had it expected Mr Mitterrand to leave office.
Francois Leotard, another UDF leader and opponent of Mr Giscard d'Estaing, said earlier that it was important not to damage the institution of the presidency itself, hinting that it would be wiser for future stability not to push Mr Mitterrand towards the door.
Yesterday, the state France 2 television channel questioned whether the Elysee leaks about the appointment of a UDF prime minister were info ou intox - news or disinformation. Mr Giscard d'Estaing and Mr Leotard would be the obvious UDF candidates.
Until now, the nomination of Edouard Balladur, a faithful Chirac lieutenant and former finance minister under the 1986-88 'cohabitation' when Mr Chirac headed the government, has been almost a foregone conclusion. The daily Liberation reported that Mr Balladur had worked out a government list, dividing ministries equally between the RPR and UDF.
Some Gaullists, particularly Charles Pasqua, one of the leaders of last year's campaign against the Maastricht treaty, have said they believe that Mr Chirac should become prime minister if offered the post.
In 1986, Mr Mitterrand nominated him as the leader of the largest party in parliament. The RPR is likely to be the biggest again after Sunday but Mr Chirac has said he will not serve.
Part of their logic is that to refuse it could reflect badly on a man who hopes to be the next president. They also argue that Mr Chirac is one of the few leaders who would be able to control a volatile conservative majority.
The Figaro interview showed that, whether in government or on the sidelines, Mr Chirac intended to be an influential figure. Referring to the tradition which leaves the president in charge of defence and foreign policy, he said this was not a constitutional right.
Gaullist sources said, meanwhile, that one way of containing Mr Mitterrand would be to form a sort of national security council of the president, prime minister, foreign and defence ministers, to take decisions by committee and thus limit the impact of a president who remains chief of the armed forces.
Michel Rocard, the main candidate for the presidency on the left, faces defeat in his parliamentary seat.
This means that one of the two men who Mr Mitterrand is believed to want least to succeed him appears to be eliminated as a serious presidential contender. Mr Chirac is Mr Mitterrand's other pet hate and, with Mr Giscard d'Estaing evidently anxious to re-take the presidency, this leaves the Gaullist leader facing a powerful de facto alliance.
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