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The General Secretary of the Unite union, Len McCluskey, has said an improved pay offer for airport workers was "good news" as a planned 48-hour strike in the two days before Christmas was called off.
More than 1,500 check-in staff, baggage handlers and cargo crew employed by Swissport had been due to walk-out over the dispute.
"We'll be recommending to our members an improved offer," said Mr McCluskey. "We're expecting a result fairly speedily, so I'm delighted that we've been able to arrive at the agreement."
However he said that the situation with British Airways is "still difficult".
Mr McCluskey added: "My team are working, as they have been for the past 72 hours, to try and arrive at a solution. Progress has been painfully slow.
"I would call on British Airways senior management now to get involved."
A planned 48-hour pay strike that was due to cause major Christmas travel disruption at the UK’s airports has been called off.
More than 1,500 check-in staff, baggage handlers and cargo crew across 18 airports were due to strike on 23 and 24 December in a dispute with Swissport.
Unite general secretary Len McCluskey confirmed the strike had been cancelled after an improved pay offer from Swissport.
Talks are continuing to try to avert strikes by British Airways cabin crew but Mr McCluskey said progress was "painfully slow".
Rail and Post Office workers are set to launch their second day of strikes on Tuesday.
Southern Railway members of the Rail, Maritime and Transport union will finish their 48-hour walk-out in a long-running row over the role of conductors.
Southern's 300,000 passengers will likely face fresh travel chaos.
Meanwhile, Post Office workers in the Communications Workers Union will begin their second of five days of striking over jobs, pensions and branch closures.
Efforts are also continuing to avert a British Airways Christmas Day and Boxing Day walk-out.
Amid of wave of pre-Christmas strikes, Downing Street has accused trade unions involved of showing "shared contempt" for the people whose lives are being disrupted.
A strike by Post Office workers closed about 50 High Street branches on Monday, while action by Southern Railway staff continues.
Asked whether Prime Minister Theresa May suspected the industrial action may be co-ordinated, a spokesman said: "There are a number of strikes across different sectors for a number of different reasons.
"If these strikes share one think in common, it is a shared contempt for ordinary people trying to go about their ordinary lives.
"Their actions are clearly designed to bring maximum damage and disruption during the festive period. But the motivation for the timing of those strikes is an issue for them.
"What our focus has got to be on is the people who are suffering, and how we can encourage all parties to get around the negotiating table and bring these disruptions to an end."
British Airways have said it plans to run a full service on Christmas Day and Boxing Day despite the impending strike by cabin crews.
The airline had slammed the decision by the Unite union to hold a strike over the festive period and pledged to ensure its customers get to their destinations.
Unite members have decided to take industrial action following a pay dispute of around 4,500 so-called mixed fleet cabin crew who joined the airline since 2010.
Striking Post Office workers set up a Santa's Grotto, complete with live reindeer, outside a government department at the start of a week of industrial action over jobs, pensions and branch closures.
The Communication Workers Union staged the festive protest outside the central London headquarters of the Business Department, including fake snow.
The union handed in more than 70,000 post cards signed by members of the public across the country in support of their campaign.
General secretary Dave Ward warned that the future of the Post Office in high streets was at stake because of the franchising of Crown Post Offices to retail firms such as WH Smith.
The union claimed a fresh wave of closures is set to be announced in the new year.
The Post Office said around 50 branches were closed by the strike.
The Post Office said the majority of its branches were open despite the strike.
Three hundred branches are striking, but the Post Office said around 250 of these were open.
The rest of the Post Office's network of 11,600 branches is not involved in the dispute.
Post Office group network and sales director Kevin Gilliland said: "We want to reassure customers that nearly all of our network is unaffected by the strike action."
Strikes by rail and Post Office workers are "solidly supported" according to unions.
Southern Railway RMT members have begun a 48-hour stoppage in a long-running dispute over the role of conductors.
Members of the Communication Workers Union will strike for five days this week, including Christmas Eve, in protest at job losses, the closure of a final salary pension scheme and the franchising of Crown Post Offices.
The union said there was strong backing for its campaign from the public.
General secretary Dave Ward accused the management of rejecting a peace offer and warned post offices will cease to exist on the high street if the planned closure programme continues.
Post Office group network and sales director Kevin Gilliland said: "It will be business as usual in almost all of our network, with over 50,000 Post Office people on hand to support customers as they make their preparations for Christmas."
Latest ITV News reports
A number of strikes will be launched by thousands of workers across the rail, post and airline industries in the lead up to Christmas.