President Francois Hollande has threatened Economy Minister Emmanuel Macron with the sack after he came close to declaring a challenge for the presidency.
In a TV interview to coincide with France's Bastille Day holiday, Mr Hollande said: "If you don't respect the rules, you're out".
Mr Macron held the first rally of his new political movement this week.
After he had given a speech, the crowd chanted "Macron, president!"
A former investment banker who became an adviser to President Hollande before securing the economy brief, Mr Macron has annoyed Socialist cabinet colleagues with his presidential ambitions.
His movement "En Marche" (On the Move) was set up in April as a centrist group to foster ideas.
However, he is widely seen as harbouring hopes of running for the presidency in 2017 elections. The Socialist primaries are only six months away and Mr Hollande continues to struggle in the polls.
The president's patience with Mr Macron finally snapped after days of discord in the cabinet.
'Temptations of populism'
The cabinet row burst into the open on Tuesday. Shortly before Mr Macron addressed his movement's first rally, Prime Minister Manuel Valls told reporters forcefully that "it's time to put a stop to all this".
Then, the pro-business economy minister said during an hour-long speech that France had been "worn down by broken promises" and that he realised how much "the system did not want to change".
Mr Valls responded by accusing him of not living up to his responsibilities. "You can't condemn a so-called system and give in to the temptations of populism, when you yourself are the perfect product of France's elite," he said.
Defence Minister Jean-Yves Le Drian stepped up the attack on Mr Macron on Thursday morning, speaking of the government as a football team, with the prime minister as captain and the president as coach.
"Then there are players who have to play as a team," he told RTL radio. "If the best player plays by himself, he won't score. So I wish he'd play as part of the team."
'Complete loss of authority'
Foreign Minister Jean-Marc Ayrault said the last thing France needed was a political crisis when it was in the middle of terrorist threat. And then, hours later, President Hollande threatened the economy minister with the sack.
"There are rules," he said. "Solidarity and teamwork come first; then there can be no personal initiatives, and even less presidential ones. You simply have to serve to the end."
While praising Mr Macron's ability, he said that if he failed to respect the rules of staying in the government, he would have to go.
As the political row played out across the air waves on France's day of independence, opposition Republican leader Nicolas Sarkozy weighed in by suggesting it all pointed to a complete loss of authority on the part of President Hollande.