Schools in England look set for further disruption over the coming weeks after talks to avert planned strike action by teachers ended in failure, with no new offer on the table.

Union leaders met the education secretary, Gillian Keegan, on Wednesday morning, the latest of a series of meetings. Though they remarked on a new urgency about the talks, there was still no progress on pay.

As things stand, further strike action by members of the National Education Union (NEU) planned for later this month and into March looks inevitable, one leader said. There are also warnings of a potential escalation, with other unions now considering next steps.

More talks are expected to follow, and the NEU joint general secretary Kevin Courtney said his members would not back down.

“Nothing in this meeting gave us anything we could work with to justify suspending the next day of regional strikes on the 28 February,” he said. “Gillian Keegan and the government need to be aware that teachers will not back down on this. Decades of an education system being run into the ground and below-inflation pay increases over the past decade have left the profession utterly demoralised.”

After the teachers’ strike on 1 February which closed thousands of schools, NEU members in the north of England, Yorkshire and Humber are due to go on strike on 28 February, followed by a day of action in the Midlands and east of England on 1 March, and one in London, the south-east and south-west on 2 March. Another two days of action on 15 and 16 March will involve all eligible NEU members in England and Wales.

“We cannot go on like this,” said Geoff Barton, the general secretary of the Association of School and College Leaders, whose members have voted in favour of a formal ballot on industrial action. “While the tone of today’s talks signalled a greater sense of urgency on the part of the government, we have to report that once again there is no new offer to improve the inadequate pay settlement which has sparked the ongoing dispute.

“Unless there is tangible progress towards an improved offer, the prospect of further strike action by NEU members is inevitable, and will lead to members of our union, and other education unions, also concluding that industrial action is the only option left. We have held off from that step and tried to resolve the dispute through negotiation. However, there is a limit to how many times we can come out of a meeting with the education secretary without progress being made.”

Barton said the Welsh and Scottish governments had made improved offers. “Those offers might not be perfect and won’t satisfy everyone. But they are a great deal better than anything managed by the government in Westminster, which has put nothing on the table so far despite having far more resources at its disposal,” he said.

NEU members in Wales had been due to strike on Tuesday but their action was suspended to consider the Welsh government’s new offer of an additional 1.5% pay rise plus 1.5% as a one-off payment, which they rejected. The strike will now go ahead on 2 March.

Scotland’s biggest education union, the EIS, is considering a revised offer including a 6% pay rise in the current year and a further 5.5% in the new financial year, which starts in April. The next national strike is due to be held on 28 February and 1 March.

NEU members are striking in pursuit of an above-inflation pay rise funded by the government rather than out of existing school budgets. The government announced last summer that most teachers would receive a pay rise of about 5%, with starting salaries up by 8.9%.

A Department for Education spokesperson described the talks as constructive, adding: “The education secretary instructed officials to hold further detailed talks with unions and committed to more talks ahead of planned strike action.”