A 48-hour walkout was staged by security staff at 11 airports operated by Highlands and Islands Airports (Hial) last week as part of the industrial action, which saw flights cancelled at Dundee airport.
Hial bosses said they would make a formal offer to "resolve this issue as quickly as possible".
The Prospect union welcomed the move.
Hial, which is owned by the Scottish government, operates airports in the Hebrides, Orkney and Shetland, Dundee, Argyll, Inverness and Wick.
About 120 staff from security company AMSL took part in industrial action last week as part of a dispute over pay.
Hial managing director Inglis Lyon said he hoped the issue could be swiftly resolved.
He said: "We will submit a formal offer to the union this week which we hope will provide the basis for a meaningful, constructive dialogue.
"It has always been the intention of the company to address the concerns of security staff, but it is impossible to do so under the threat of industrial action.
"It is important that we resolve this issue as quickly as possible. The threat of further industrial action is in no one's interests, particularly as we approach the busy summer season."
Prospect national secretary Alan Denney said he was "pleased" that Hial had "made progress".
He said: "We look forward to receiving a written offer and entering into a constructive dialogue with Hial on the basis of this. We hope this will lead to a swift resolution of our dispute.
"The legal mandate for further strike action remains, but if Hial makes a reasonable offer which addresses our objective of securing equal treatment for AMSL workers, we should not need to exercise that option."
Prospect represents 120 of AMSL's 160 workers at the 11 Hial airports.
Talks are to be held in a bid to prevent further strike action at Scottish local airports.