By james art The workers were due to take action on Friday night and on several days in the coming weeks in a pay dispute.
The RMT said it had received an offer of improved pay.
Strikes by members of the Aslef drivers’ union next week and later in the month are still planned to continue.
An RMT spokesman said: “Following intensive negotiations with London Underground management and a significantly improved offer, we have suspended the strikes planned to start tonight.
“London Underground has sensibly backed down from their proposed changes to pay structures, which now means that all our members will receive equal value in every reward.
“Further discussions will take place next week on the pay proposal, but progress has been made which would not have been possible without the courage and industrial strength of our 10,000 members across London Underground.”
Clare Mann, chief operating officer of Transport for London, said: “We are delighted that the RMT has suspended its planned industrial action on the London Underground network to allow further negotiations. We believe our offer is fair, affordable, good for our colleagues and good news for London.
“We will continue to work closely with all our unions and insist that Aslef also cancels the planned action next week. If this happens, customers should check before they travel as there will be almost no service during their strikes on 7 and 12 November.’