HP staff represented by the Public and Commercial Services (PCS) union have suspended the strike action scheduled for today and tomorrow at HP while mediation continues.
The strike was called off on Friday after talks at the Advisory, Conciliation and Arbitration Service (ACAS) on 25 March.
Jim Hanson, national officer at PCS, said: "We had talks last week that were quite successful and we will have more talks tomorrow. We haven't got a final offer yet, so we are mid-way, but the talks have been positive enough to suspend the action."
However, Hanson added that the strike action scheduled for 6 and 7 April was still possible, depending on the results of tomorrow's talks with ACAS.
If they go ahead, the strikes will take place in the north east and north west of England, and will affect HP Enterprise Services' IT contracts for the Department for Work and Pensions, the Ministry of Defence and General Motors.
The industrial dispute centres on the company's pay freeze and redundancies - some 3,400 EDS staff have been made redundant since HP took over the company in 2008, and a further 1,000 job losses are planned for the first half of this year.
The dispute between PCS and HP has been going on since December 2009, when HP narrowly avoided a strike by union members by agreeing to sit down to talks at the eleventh hour.
After a one-day strike in January, Hanson said the union had had a couple of meetings with the mediation organisation Advisory, Conciliation and Arbitration Service (ACAS), but that HP "wasn't willing to move far enough."