Unite members went on a 24-hour strike last Monday (26 September) after a breakdown in negotiations over a pay freeze implemented two years ago.
But, two further strikes planned for yesterday (3 October) and next Monday (10 October) were postponed.
Unite national officer Steve Sibbald said: "The strikes have been suspended for seven days pending talks between chapel representatives and the company. We are hopeful that we can get a resolution in the next week."
Holographics managing director Stephen Clarke said: "We are pleased that the employees have chosen to suspend industrial action for seven days to allow further discussions to take place next week.
"Our priority continues to be making sure that our customers can rely on API Holographics for product quality and service."