The conciliation service Acas announced that leaders of the Unite union and officials from six distribution companies will meet on Monday.
Unite has also been given an extension to next Tuesday before it has to make a decision about calling industrial action.
The two sides have already held six days of talks but tanker drivers' representatives overwhelmingly turned down a proposed agreement yesterday despite progress being made on some of the issues involved in the row.
ITV News has obtained details of the offer at the centre of the petrol tanker row, ahead of talks to avert strikes by fuel tanker drivers.
The unions may have to re-ballot over the tanker strike dispute, as the original ballot may be based on a flaw.
The union Unite are facing a Friday afternoon deadline on whether or not to call industrial action in the fuel tanker driver dispute.