Progress has been made in talks aimed at improving industrial relations and averting a threatened Tube strike.
Two 24-hour walkouts had been planned
Rail union Aslef said a walkout would be unhelpful and could harm talks over industrial relations with London Underground (LU) bosses.
But the Rail Maritime and Transport (RMT) union said its executive would meet on Tuesday to reach a decision.
Last week, the unions called off the first of two co-ordinated 24-hour walkouts following talks.
The row covers various issues from LU's policy on signals passed at danger (Spads), to health and safety, alleged harassment and bargaining arrangements.
An Aslef spokesman said any action would be suspended for four weeks, during which time they expected to resolve the dispute.
"The negotiating team has reached provisional outline agreements with the company on all outstanding issues and the action has been suspended with the clear expectation the details will be ironed out within the next 28 days," he said.
"If this does not happen we will have been misled and cheated. It would lead to a vigorous and sustained reaction from Aslef."
An RMT spokesman said: "We have had talks with London Underground today. We are now waiting for something in writing from them."
An LU spokesman said it was pleased Aslef had recommended that the strike was called off, saying constructive talks had taken place with both unions on Monday.