London Underground has invited union leaders to talks next week in a bid to resolve a dispute over pay and hours which led to strikes.
The company said it wanted to hold talks next Wednesday.
Tube services are expected to return to normal by late morning on Friday after the strikes which have caused travel chaos all week.
Members of the Rail, Maritime and Transport union (RMT) walked out, leading to services been crippled since Monday with few underground trains running.
Commuters have switched to buses, bikes or trains not affected by the dispute to get to and from work.
London Underground said there will be no service before 8am on Friday, with normal service on all lines by late morning.
The Docklands Light Railway will be running a normal service after it was hit by a strike over a separate issue on Thursday.
An RMT source said: “This is a step in the right direction from TfL (Transport for London) and has only occurred due to the industrial pressure from RMT members this week.”
Commuters trying to get home on South Western Railway also suffered delays due to a tree blocking the railway between Clapham Junction and Earlsfield, which led to some lines towards Wimbledon being blocked.
SWR said it expected there may be cancellations, delays or alterations to services until 8pm.
SWR services towards Putney were also blocked because of a fault on a train at Clapham Junction, with delays or alterations expected until 6pm.
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