Leading figures in the ruling French socialists have rushed to avoid a damaging split over their candidate in next year's presidential election, reports the BBC.
Alarm bells sounded after prime minister Manuel Valls suggested he might stand against President François Hollande in party primaries.
However, the two had lunch together on Monday in a "cordial" atmosphere, Mr Hollande's office said.
François Fillon was elected as the conservatives' candidate on Sunday.
He triumphed at party primaries, winning 66.5% to 33.5% for his run-off rival, Alain Juppé.
A new opinion poll suggests he would easily beat the far right's Marine Le Pen in the actual election, held over two weekends in April and May.
According to the Harris Interactive poll for French parliamentary TV, Mr Fillon would lead the National Front candidate by 26% to 24% in the first round, then win the run-off against her by 67% to 33%.
The same poll indicates that Mr Hollande or Mr Valls would win just 9% for the socialists, leaving them trailing the far left and the centrists.
Mr Valls said on Sunday that he would not rule out running against Mr Hollande in the primary, telling the Journal du Dimanche he wanted to dispel the idea that the left had "no chance" of retaining power.
But government spokesman Stéphane Le Foll stressed that Mr Valls would need to resign in order to stand.
"There will not be a primary between the president and the prime minister," he told Europe 1 radio.
At his weekly lunch with the president, Mr Valls apparently played down the idea of resigning, reportedly telling Mr Hollande: "I am head of the government, my instincts lie with the state."
The Elysée Palace said the two-hour lunch had taken place in a "quite cordial and businesslike atmosphere".