Members of the Public and Commercial Services union (PCS) have taken more than 60 days of action after claiming the employer was withholding a cost-of-living payment.
The £1,500 payment was part of the Government’s pay offer for 2022/23.
Following talks this week, the PCS is putting the employer’s improved offer to a ballot of all members.
Strike action due to take place during half-term next week (May 28 to June 2) has been suspended.
NML comprises eight different venues, including the Lady Lever Art Gallery, located in Port Sunlight.
PCS general secretary Fran Heathcote said: “Our members at National Museums Liverpool were furious at being excluded from a cost-of-living crisis payment that was paid to civil servants following our national campaign.
“They then went out on picket lines in all weather conditions to fight for what they deserved.
“It is down to their remarkable determination and creativity that we have negotiated an offer from management which we will put to a vote of all NML members involved in the dispute in the coming days.”