Members of the RMT union at London Underground have called off plans to strike over the coming week, as transport officials urged tube train drivers to follow suit.

The RMT said it had suspended its planned week-long action, which had been due to begin on Friday evening, after receiving a significantly improved pay offer from tube bosses.

Aslef, the train drivers’ union, has yet to call off plans for a highly disruptive strike by tube drivers next Thursday and another the following Tuesday, but the Guardian understands it will meet London Underground on Monday for talks.

Transport for London urged the union to take a cue from its fellow union and call off the action.

A spokesperson for the RMT, whose members include signalling and station staff, said: “London Underground have sensibly abandoned their proposed changes to pay structures, which now means all our members will receive the same value in any pay award.

“Further discussions will take place next week regarding the pay offer but progress has been made which would not have been possible without the fortitude and industrial strength of our 10,000 members on London Underground.”

Before the strike was called off, RMT maintenance staff had been due to strike for 24 hours from Friday evening. Track access controllers and control centre staff were to stage a 24-hour walkout on Saturday, and its emergency response unit was expected to do the same on Sunday.

This would have been followed by train staff, engineers and controllers striking from Monday to Wednesday, with TfL warning of severe disruption, with most lines not running on Tuesday and Wednesday.

Driver and management staff members at Aslef are still on course to walk out on 7 and 12 November, with TfL warning that no service is set to run on these days. Some members who drive maintenance trains will still stop work for 24 hours from 6pm on Friday.

Scheduled tube strikes have been called off before taking place in recent months. An Aslef strike planned for May was called off in April after the union said a TfL proposal resolved the key issues in the dispute.

Rail passengers on national routes also received some respite from industrial action after Aslef and RMT members voted in September to accept pay offers, ending a long-running dispute that had disrupted services across the country for more than two years.

Claire Mann, TfL’s chief operating officer, said: “We are pleased that the RMT has suspended its planned industrial action on the London Underground network to allow further talks. We believe that our offer is fair, affordable, good for our colleagues and good news for London.

“We will continue to work closely with all our trade unions, and urge Aslef to also call off its planned action next week. If it goes ahead customers should check before they travel as during their strikes on 7 November and 12, there will be little to no service.”