Bridgman added bargaining on a new contract with the PSA has been under way for several months.
"The ministry remains open and committed to reaching a negotiated settlement and we're ready to meet at any time," he said.
The ministry has offered a 5 per cent increase over two years, in line with other agreements in the public sector.
However, the PSA has requested an increase of more than 13 per cent.
The union earlier said it also sought to close the gender pay gap for ministry workers.
The average female employee at the ministry is paid 15 per cent less than the average male worker, the PSA said.
It is a larger gender pay gap than the average public sector department of 12 per cent.
"The PSA believes the ministry does not properly value some female-dominated roles - and our efforts to strike a deal to reduce this pay gap and have staff properly valued have so far come to nothing," PSA national secretary Erin Polaczuk said.