Mr Chirac has responded to appeals for calm from Mr Balladur by implying that the Prime Minister should drop out of the presidential race, and insisting that any meeting between the two should be convened by him.
Earlier this week, Mr Balladur embarked on a series of meetings with his ministers and parliamentarians of the ruling conservative coalition to limit the damage, after allegations of political corruption forced one minister to resign and led to the detention of a former cabinet member.
Mr Balladur repeated a request to ministers not to get involved in the campaign for the presidential election - to choose a successor to the Socialist Francois Mitterrand when his mandate ends next May - until the New Year.
Then, Mr Balladur wrote to both Mr Chirac, the president of his Gaullist RPR party, and Valery Giscard d'Estaing, the head of the centre-right Union for French Democracy (UDF), asking for a meeting to discuss ways of cooling the atmosphere.
Mr Giscard d'Estaing replied in a press statement that his party had not provoked the turmoil which Mr Balladur wished to calm. Mr Chirac responded by virtually summoning the Prime Minister to a conference with Gaullist leaders. But first, he implied, Mr Balladur should drop out of the presidential race.
'I am convinced,' wrote Mr Chirac, 'that your action, to be effective, must remain above all quarrels. Nothing should interfere with government work at a time when the constraints of (left-right) cohabitation and the approach of a presidential election are already weighing on it.'
If the suggestion that Mr Balladur should concentrate on his work as Prime Minister rather than involve himself in the presidential campaign were not enough, the next sentence made it impossible for the two men to meet.
'Of course, I am ready to meet you one-on-one,' Mr Chirac continued, 'but it is first necessary to take stock within the political family to which we both belong. To this effect, I propose to bring together the main leaders at a date in the near future which would suit you.'
Mr Balladur's reply came through Nicolas Sarkozy, the Budget Minister and government spokesman. Party leaders in the French Republic, he said, 'don't make the running'. Mr Balladur should not get involved in 'polemics' and when Mr Chirac and Mr Giscard d'Estaing 'want to come, they will be welcome'.
The episode was a clear rebuff to Mr Balladur. By first talking to his most difficult ministers and then meeting members of both coalition parties before talking to the full cabinet on Tuesday, he wanted to assert his authority as the head of the conservative coalition.
Mr Chirac's refusal to be seen to be going to the Prime Minister's office to hear the same lecture no doubt ended all pretence at good relations between the two men. Mr Balladur became Prime Minister last year with Mr Chirac's blessing, because the RPR leader apparently believed he could position himself better for the presidency in 1995 by staying outside government.
Mr Balladur, who has never said that he will be a candidate, has enjoyed consistently good poll ratings, making him the commentators' favourite to take the Elysee Palace next May.