The union representing Aer Lingus pilots believes a resolution can be reached to the row over the airline's plans to establish a new base in Belfast later this year.
However, assistant general secretary of Impact Michael Landers said the union should have a role in negotiating the pay and conditions of pilots recruited for the new Aer Lingus operation.
Talks between senior Aer Lingus management and representatives of pilots on the dispute, which almost led to a 48-hour strike last month, were adjourned yesterday after about two hours.
The talks may resume on Wednesday.
Sources suggested yesterday that the parties had put forward various proposals and that these would be considered over the next few days.
Speaking after the talks at Aer Lingus headquarters in Dublin airport, Mr Landers described yesterday's meeting and the fact that further negotiations were scheduled for later in the week as positive developments.
"We have agreed that we will meet again, so obviously the issues continue to be under discussion between ourselves and the company. I think that is positive and the way to an ultimate resolution of all these issues.
"I think the atmosphere is constructive. I think we are trying to reach a resolution and think we will be able to do that in the end," he said.
Mr Landers said that there was no particular timescale for reaching a conclusion to the current talks, although he said there were time pressures on all sides.
"Our efforts are aimed at getting this right," he said.
Mr Landers said there had been no discussions on the announcement last week by Ryanair, which owns nearly 30 per cent of Aer Lingus, that it is also to establish a new base in Belfast.
He said the current talks were about Aer Lingus and not Ryanair.
Asked whether the union still believed it should have a role in negotiating the terms and conditions for pilots in Belfast, Mr Landers said: "Clearly that has always been our position and is going to remain our position."
The issue of whether Impact and the pilots' representative association Ialpa should be involved in negotiating terms and conditions is at the heart of the current dispute.
Aer Lingus has argued that there should be no role for the union in negotiating terms to apply to new staff working outside of the Republic.