If no solution is found, thousands of workers are planning to walk out for 24 hours from 8pm on September 24 and again from 8pm on October 1.
RMT members, including station and signalling staff, voted earlier this month in favour of industrial action in protest at an imposed 3% pay rise.
Aslef announced today that drivers had also backed a series of walkouts. The union's general secretary, Mick Rix, said: "London Underground managers have attempted to impose an unacceptable pay offer on our members without regard to the proper conduct of industrial relations."
Mr Rix accused the company of refusing to take the dispute to arbitration and said managers were harassing local union officials.
London Underground said it could not improve its pay offer of a 3% increase. That offer would boost the pay of train drivers to £31,000 per year.
"We have awarded a 3% deal to all our staff after exhausting all reasonable negotiations with our union colleagues," London Underground's human resources director, Bob Mason, said before the unions' announcement.
"It's a good deal. It's a fair deal and strike action will not change that fact," Mr Mason said.
The joint action by members of the Rail Maritime and Transport union and the drivers' union Aslef could cause major disruption to London's tube network, which carries around 3 million passengers per day, causing widespread chaos across the capital.
