Speaking after talks, he said there was "the possibility of agreement" in some areas, but key divisions remain.
Civil servants' union leader Mark Serwotka said "not one jot of progress" had been made on demands for staff to work longer and contribute more.
Up to 750,000 teachers and civil servants are set to strike on Thursday.
That action will still go ahead, involving members of the National Union of Teachers (NUT), the Association of Teachers and Lecturers (ATL), the University and College Union and the Public and Commercial Services (PCS) union.
The walk-out, in England and Wales, is expected to disrupt thousands of schools.
Mr Serwotka - whose PCS union represents 300,000 civil servants, including coastguards, tax officials and court and job centre staff - said the government had shown "no interest in actually negotiating on any of the key principles at the heart of this dispute".
'Some movement'Mr Barber agreed there were still major divisions between unions and the government over three key proposals - to raise the pension age, to increase workers' contributions and to link pension values to the generally lower consumer prices index (CPI) rather than the retail prices index (RPI).
The government has, however, said it will enter into separate discussions over the local government pension scheme, after unions warned that many members could opt out altogether if made to contribute much more - putting the whole existence of the scheme potentially at risk.
Continue reading the main story Norman Smith Chief political correspondent, BBC Radio 4For all Mr Gove's tough talk - and dire warnings from some union leaders of a repeat of the 1926 General Strike - there's little desire on either side for a showdown.
Instead, though Thursday's strikes will go ahead, there is a clear preference to keep talking.
From the union perspective, they are acutely aware of the difficulty in sustaining any prolonged strike action at a time when many members are already struggling with pay cuts and high food and fuel costs.
On the government side, while some Tories would relish a symbolic "victory", the predominant view appears to be that ministers have more pressing issues.
Strikes are at their lowest level for a generation and ministers acknowledge the industrial landscape is different to that faced by Mrs Thatcher in the 1980s. The unions are no longer seen as a significant problem.
Both sides therefore have a strong incentive - for the time being - to keep on talking.
Mr Barber welcomed this development and said that, more broadly, ministers had indicated "some movement in their thinking on some issues"."They are trying to look at ways of giving greater assurance that the value of people's pensions will be maintained," he said.
He added that more talks would talk place in July and the TUC was committed to taking part in them to try to reach an agreement.
The public sector union Unison - which represents more than 1.2 million workers - had warned that it would ballot its members for strike action if the talks proved unsatisfactory.
But Unison's leader Dave Prentis said that while "a massive cavern" remained between the two sides, no ballot would be called.
"I think we found today the government were willing to treat the negotiations seriously," he said.
"We thought that today may be the last day and we would be moving into conflict this evening, [but] they've agreed to two further meetings in July and we hope to negotiate through July.
"We'll make a decision based on the outcome of those negotiations."
Cabinet Office Minister Francis Maude described the talks as "constructive".
"This is a genuine consultation to which we are committed in order to try and agree a way forward with the unions, including on how to implement the changes on contributions set out in the spending review," he said.
On the local government scheme, Mr Maude said: "We recognise that the funding basis for the local government pension scheme is different.
"There are important implications for how the contributions and benefits interact... On that basis, we have agreed to have a more in-depth discussion with local government unions and the TUC about how we take these factors into account."
'Duty' to keep schools openThe government has insisted it has contingency plans in place to prevent any major disruption to essential services on 30 June.
But Education Secretary Michael Gove has been criticised after suggesting that parents should go into schools to help keep them running.
The prime minister's spokesman has since tried to clarify the matter: "Michael Gove simply said schools should make every effort to stay open to minimise inconvenience.
"This is not something we are doing from Whitehall - schools themselves should look at every option for staying open."
Mr Gove has also warned that the teaching profession is risking its reputation by striking and last week, he wrote to head teachers saying they had a "strong moral duty" to keep schools open during the strike.
Teachers have been working out how much the change will cost them A teachers' union is mounting a High Court challenge to government changes to their pension scheme.