Industrial action planned for Monday has been called off, and both sides have now said that they are optimistic that a deal can be reached to avoid any further walk-outs.
Unions had branded a 4% pay offer "unacceptable", but library managers said their offer was above average, and benefited the lowest-paid workers most.
Two days of "selective" action by audio visual staff on Tuesday and Wednesday were also called off as negations got back under way.
A strike in late July closed reading rooms at the library's main site in St Pancras, London, while two further days of action affected services at the Boston Spa complex in West Yorkshire in early August.
"We are hopeful that the suspension of strike action will provide an opportunity for a fair pay settlement to be reached," Neil March, of the Public and Commercial Services (PCS) union said.
A statement said that both sides were "heartened" by the return to the negotiating table, and were keen to avoid further disruption to services.
PCS members accepted a pay rise of 3.6% in August 2001 on the basis that a further increase in salary would follow.
However, the union said the latest offer of 0.4% - giving an overall pay increase of 4% - was unacceptable to its members.
The library insisted the pay offer has already been accepted by two of the three unions that represent staff at the library.
'Important'
The library's lowest paid workers earn as little as £12,000. Library bosses are insisting that their lowest-paid staff will receive a 5.6% pay rise and the 4% rise is just the average across all the staff.
"PCS represents the lowest paid workers at the British Library. That they lost pay to support the strike demonstrates how important this issue is to them," Mr March said.
The British Library's head of human resources, Andy Cook, said he was "very pleased" that the action had been suspended.
"We now have a real opportunity to jointly address the issues that face the library. As well as pay, the discussions will include modernising the library's pay and grading systems and HR policies and practices," he said.