"Courage is not obstinacy, it is listening, understanding," Ayrault said after an emergency meeting with politicians and civil servants from Brittany, where protests have seen clashes between demonstrators and police.
But, he insisted, the decision is a "suspension, not a cancellation".
MPs and local councillors from the right-wing UMP party boycotted the meeting, calling for the tax to be scrapped.
Reminding them that the tax was brought in when the UMP was in power and Nicolas Sarkozy was president, Ayrault called for dialogue between "those who yesterday voted for it, dreamt it up, and we who today have to put it into practice".
Transport Minister Frédéric Cuvillier indicated that the tax, which shoud have come into force on 1 January 2014, would be suspended for "several months", while its consequences for farming, the food processing industry and far-flung regions like Brittany are assessed.
President François Hollande, who is on an official visit to Slovakia, told reporters that he had given Ayrault responsibility of deciding how to handle the question, although government sources say that he had the final decision.
The tax, which had all-party support when it was agreed by the National Assembly, will impose new levies on French and foreign vehicles transporting commercial goods weighing over 3.5 tonnes.
Its postponement is the government's second climbdown on proposed taxes within a few days.
Employers' and farmers' unions welcomed the announcement, while calling for the suspension to last until the current economic crisis is over.
On Sunday it scrapped tax rises on savings plans.
Under European Union pressure to reduce the state deficit, Hollande's government has announced about three billion euros of tax rises for next year, arousing vocal opposition from both the mainstream right UMP and the far-right Front National.