Ayrault said there will be no new operating permits for private hire cabs, known as VTCs while a mediator, appointed on Wednesday tries to work out a solution to the conflict.
Cabbies claim the VTCs are competing unfairly because they are subject to limited government regulation, while taxi drivers must contend with steep license fees, a government-fixed fare structure and other constraints.
For the third day in a row strike action began early on Wednesday, with some 70 taxis blocking pick-up spots at Orly airport south of Paris and a convoy slowing traffic from Charles de Gaulle airport north of the capital.
Salt was rubbed into taxi drivers' wounds last week when a government plan to impose a 15-minute delay before VTCs could pick up their passengers, was thrown out by the Council of State.
The taxi unions are calling for VTCs to be limited by a 30-minute delay and a minimum fare of €60 ($82) - which would effectively close them out of the market for trips within central Paris.
Cabbies say they will continue to protest until the government puts a block on handing out new licenses to VTCs.
After holding a strike on Monday that brought the peripherique to a standstill as well as the main roads from Paris' two airports, taxi drivers continued to protest on Tuesday.
One hundred drivers blockaded Place de La Concorde before moving on to Gare du Lyon. According to RMC radio 64 drivers were arrested by police overnight when officers moved in to break up the blockade. They were later released without charge.
A new national day of mobilization has already been set for March 13th.
For its part the government has appointed a mediator Thomas Thévenoud, who has the unenviable job of trying to bring the two sides together.
On Wednesday he called for calm, saying the message from taxi drivers "has been heard loud and clear".
"I call on everyone to gather around the table with me, to talk, to listen, to compromise and to find a new system," he told BFMTV.
Thévenoud has been mandated to come up with a system of "balanced competition" between taxi drivers and VTCs within two months.
Taxi drivers have for years jealously guarded their right to operate on the streets of Paris, leading to accusations of artificial shortages in the French capital.
Licenses are granted by the government for free, but in limited numbers, and are sold among drivers for around €230,000 ($315,000).
The license to operate a VTC costs only €100 ($136).