The talks follow a crisis meeting chaired by French President Emmanuel Macron on Sunday as he surveyed the damage from a day of riots across Paris that saw violence “on a level not seen in decades.”
Philippe has been asked to meet protest organisers and party leaders as part of a “constant wish for dialogue,” the Elysee Palace said.
Environment Minister Francois de Rugy met representatives of the so-called “yellow vest” protesters last week but failed to convince them to end the demonstrations that have taken place over the last two weeks.
The government has not ruled out imposing a state of emergency to combat the protests, which began over fuel taxes but have morphed into a broad opposition front to Macron, 40, a pro-business centrist elected in May 2017.
The president on Sunday assessed the damage at the Arc de Triomphe, the massive monument to France's war dead at the top of the Champs-Elysees avenue, where rioters scrawled graffiti and ransacked the ticketing and reception areas.
Inside, rioters smashed in the iconic face of a sculpture, a partial reproduction of the frieze “La Marseillaise” by Francois Rude.
Macron also saw the wreckage of burnt-out cars and damaged buildings from rioting at other sites, where he praised the police but was also booed by sections of the crowd.
Paris police said 412 people were arrested on Saturday during the worst clashes for years in the capital and 378 remained in custody.
Paris police chief Michel Delpuech said the violence had been “on a level not seen in decades.”
A total of 263 people were injured nationwide, including 133 in the capital, 23 of them members of the security forces.
“I will never accept violence,” Macron said. “No cause justifies that authorities are attacked, that businesses are plundered, that passers-by or journalists are threatened or that the Arc du Triomphe is defiled.”
The violence has caused deep concern in the French business community which claims it has already lost billions of euros, and representatives are set to attend a meeting at the economy ministry on Monday.
“Our worst fears have been confirmed: this is the third consecutive weekend of (protest) blockades which amounts to a major loss for the whole business community,” Jacques Creyssel, representative of a federation of retail businesses, told AFP.
'Yellow vests will win'
Three people have died in incidents linked to the anti-government protests, which were sparked initially by a rise in taxes on diesel.
In Paris on Sunday as groups of workers set about cleaning up the mess from the previous day, the scale of the destruction became clear.
Around famous areas including the Champs-Elysees, the Louvre museum, the Opera and Place Vendome, smashed shop windows, broken glass and the occasional burnt-out car were testament to the violence.
Dozens of cars were torched by the gangs of rioters, some of whom wore gas masks and ski goggles to lessen the effects of police tear gas.
One person was in a critical condition after protesters pulled down one of the huge iron gates of the Tuileries garden by the Louvre, crushing several people.
Nearly 190 fires were put out and six buildings were set alight, the interior ministry said.
Graffiti was daubed at the Arc de Triomphe, with one slogan saying: “The yellow vests will win.”