The City Council has given the German giant a three-week deadline to find a solution to a raft of problems on the job which have led to delays and cost over runs.
The project was originally due to finish in August 2011. It is now seven months behind schedule and believed to be £100m over budget.
Gordon Mackenzie, Edinburgh City Council’s transport convener, said: “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 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.”