Talks to prevent a national rail strike have been adjourned until Monday, in a dispute over pay that previously threatened a strike last Monday.
Rail, Maritime and Transport (RMT) union general secretary Mike Cash dubbed a new pay offer by Network Rail "unacceptable".
The move meant that a new 24-hour strike is planned for Thursday 4 June, as well as a further 48-hour strike from 9 June.
After last Monday's strike was cancelled so that union bosses could consider a new pay deal, the new offer was rejected on Thursday.
Both sides have been talking with conciliation service Acas since Friday. As well as the planned strike action, workers are also planning to ban overtime from 6-12 June.
Network Rail originally offered a four-year deal of a single £500 payment followed by three years of rises in line with inflation. The revised offer covered two years - with a one per cent rise in the first, and a rise of approximately 1.4 per cent next year.
The discussions also established that there would be no compulsory redundancies over that period.
The RMT's 16,000 members at Network Rail work across the company's operations and maintenance departments.
RMT boss Mike Cash had previously told his members:
RMT is fully committed to achieving a negotiated settlement and will be available in London for discussions for the whole weekend and beyond in order to achieve a settlement.
However, transport secretary Patrick McLoughlin condemned the strikes, dubbing them "unnecessary and unreasonable".