The Rail, Maritime and Transport (RMT) union has called on London mayor Boris Johnson to hold "direct talks" to avert two 48-hour strikes by Tube staff.
Union members employed by maintenance firm Tube Lines plan to walk out on 23 June and 14 July in a dispute over jobs, pay and conditions, the BBC has reported.
Work is being taken over by Transport for London (TfL) at the end of June, and the union claims jobs will be at risk.
The mayor's spokesman told the BBC that he has "made it clear he will not meet with unions".
The planned strike would "severely" affect services on the Piccadilly, Northern and Jubilee Lines, the union warned.
Upgrade work and maintenance on the lines are currently done by contractor Tube Lines.