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Members of the Public and Commercial Services union (PCS) will take action at Ty Felin and Morriston in Swansea.
The workers, who print materials for DVLA and other Government departments, went on strike in February.
The union said the walkout is likely to lead to backlogs for driving licences and tachographs.
The union has been given an improved offer aimed at ending the dispute, including the promise of a £1,500 payment to each member.
PCS general secretary Mark Serwotka said: “None of our members can be left behind, which is why we’re continuing our strike action until every employer has agreed to pay the £1,500 as quickly as possible, without any conditions.
“Ministers would be foolish to underestimate our determination to get the best for our members.”
A DVLA Spokesperson said: “We have taken steps to minimise any disruption as a result of this targeted industrial action in our print and mailing section.”
