Workers had been set to strike next week over the threat of up to 100 redundancies, over half the workforce.
Euro Packaging, which is based in Birmingham, said that redundancies, due to a downturn in demand and increased costs, were still being considered.
GPMU deputy general secretary Tony Burke said the packaging company had threatened to move work out of the UK, and initially refused to co-operate on union recognition.
The company said it had no objection in considering union recognition, and this was now under consideration.
Burke said discussions were now ongoing between the GPMU and management, and the outcome would be reported to staff on 25 April.
A majority of the 170 Sparkbrook-based workforce had opted to join the union Burke said, which had prompted the threats from the management at the plant.
"Our members along with ACAS have tried to negotiate with the company, but every time we took one step forward we took two back," he said.
Burke said the company had been looking for confrontation rather than consultation, by using the threat of job losses to scare the workforce.
Workers at the plant had opted to join the GPMU following a campaign by the union to seek recognition at the company.
Euro Packaging supplies a number of major supermarkets in the UK, including Tesco, ASDA, Woolworths, Sainsbury's, Superdrug and Ikea.
It is one of the largest manufacturers of paper bags in the UK, producing over 75m per week. It owns paper and polythene manufacturing plants in the UK and Malaysia.
Story by Andy Scott