Bartels said pilots would return to work on Tuesday although it would take time for normal operations to resume.
Joerge Handwerg, a spokesman for the Vereinigung Cockpit (VC) union representing the pilots said the union was "happy with the agreement because Lufthansa now has to resume negotiations without preconditions'.
More than 4,000 pilots had gone on strike at midnight on Monday over concerns that cheaper crews from Lufthansa's subsidiaries in other countries could eventually replace them, concerns Lufthansa said were unfounded.
The union also wants a 6.4 per cent pay rise, more say in company decisions and commitments that pilots would keep their jobs when Lufthansa shifts passengers to cheaper, foreign affiliates.
The suspension of the strike is not the end of Lufthansa's woes.
Late on Monday, Germany's UFO cabin crew union said it was considering walkouts of its own "in the coming weeks".
And travellers in Europe face more disruptions ahead as five unions representing French air traffic controllers on Monday announced a four-day strike beginning on Tuesday.
France's aviation authority ordered airlines to cancel half their flights at Orly airport and a quarter at Charles de Gaulle in Paris.
French carrier Air France said it would maintain all of its long-haul flights during the strike, with the protest movement affecting only its routes within France and Europe.
British Airways faced a renewed threat of cabin crew strikes, after the Unite union announced that most of its members had voted in favour of a walkout.
Britain's biggest labour union said after the vote that its members would meet on Thursday to discuss the ballot result before deciding on a strike date.
A previous strike threat by BA cabin crew, planned for the Christmas and New Year holidays, was cancelled only after the airline obtained an emergency court injunction to block it.
And Eurostar, the main train alternative to planes between Paris, Brussels and London, experienced an embarrassing train failure when a Paris-to London train broke down in southern England late on Sunday.
The failure plunged more than 700 passengers into darkness, forced them to climb down ladders on to the track to a replacement train, and caused them to arrive in London more than four hours late.