Most London Underground services remain suspended as a walkout by staff continues for a fourth day.
Thousands of members of the Rail, Maritime and Transport (RMT) union are carrying out a "rolling strike" in a dispute over pay and its unmet demand for a shorter working week of 32 hours - which Transport for London (TfL) says is "unaffordable".
About 90 Tube stations opened on Wednesday - at the ends of the Northern, Central, Metropolitan and District lines - but most routes through central London are closed.
The RMT union general secretary Eddie Dempsey has repeated his calls for the mayor of London to intervene and help resolve the dispute. Sir Sadiq Khan has been approached for comment.
Service has resumed on the Docklands Light Railway (DLR) after it was suspended due to strike action on Tuesday, while the Elizabeth and Overground lines remain open.
The Hammersmith & City and Circle lines are operating between Hammersmith and Edgeware Road, TfL says.
TfL said it had offered staff a 3.4% pay rise, but that shorter working hours would be "unaffordable", with a 32-hour week predicted to cost the network around £200m per year.
The RMT union said it did not expect an 32-hour week immediately, but wanted a gradual reduction.
Speaking at the TUC Congress in Brighton, Mr Dempsey called on Sir Sadiq to attend a summit with the union in a bid to find a resolution.
"I've got a message for the mayor," he said.
"Stop going on social media, invite us to the meeting, let's have a discussion, because I want to know what is going on in London."
He warned of more strike action if there was no resolution to the dispute, adding: "We take no pleasure in causing disruption but we make no apology for fighting for our members."
Nick Dent, TfL director of customer operations and head of the negotiation team, said they were "very keen" to work with RMT and wanted the union to put the 3.4% pay rise offer to its members.
"They launched their ballot before we'd made any pay offer, so members were voting without understanding what the pay offer actually was," he said.
Depot managers and signallers from the RMT are among those withdrawing their labour.
Londoners have used a combination of boats, bikes and buses to get around the capital, with a large spike in bike rental schemes.
The prime minister and the mayor of London are among those calling for both sides to negotiate after talks broke down last Wednesday morning.