Bilfinger Berger has been given three weeks by Edinburgh City Council to find a solution to the problems plaguing the Scottish capital's tram construction project, which is currently seven months behind schedule.
The £545m scheme was originally scheduled for completion in August 2011, but has been hit by delays and overspend.
Gordon Mackenzie, Edinburgh City Council's transport convener, told the BBC: "This city will not be held to ransom by this contractor any longer.
"There needs to be a move to settle the project's contractual dispute within the month.
"There would be worse things for the project than for this contract to be terminated.
"The management team at Edinburgh Trams [the company wholly-owned by the city council which runs the tram scheme] have done what they can to find a reasonable way through this dispute, but now it's time for action.
"Week after week I'm told of excessive claims, month after month progress falls behind schedule, time after time they've been told a cost plus deal is not on. The people of Edinburgh deserve better."
David Mackay, chairman of Edinburgh Trams, said: "I totally understand Councillor Mackenzie's position.
"We have been hugely frustrated by the lack of progress in settling this dispute and the subsequent lack of progress on the ground."