BERLIN/FRANKFURT (Reuters) - Lufthansa <LHAG.DE> pilots are threatening to strike after talks on pay between their union and the management of Germany's largest airline collapsed.

The union, Vereinigung Cockpit, which represents around 5,400 pilots at the company, said on Monday strike action at the main Lufthansa airline brand and its cargo arm was possible at any time, although it would give 24 hours' notice of a walkout.

Talks on new contracts for 5,400 pilots at the Lufthansa, Lufthansa Cargo and Germanwings divisions have been going on for four years and have resulted in more than a dozen strikes at one of Europe's largest airlines.

Lufthansa is trying to cut costs to cope with increased competition from low-cost carriers and leaner Gulf rivals. It has managed to agree wide-ranging deals on pay and conditions with its main cabin crew and ground staff unions in Germany.

The pilots' union said failure to agree a deal meant that its members had not had a pay increase for more than five years and that Lufthansa was offering only a pay freeze.

It is calling for an average annual pay increase of 3.66 percent, pointing to Lufthansa's profits of more than 5 billion euros ($5.4 billion) in that period.

Lufthansa, which had earlier on Monday offered mediation to resolve the impasse, said in response that the strike call was "incomprehensible".

Formal talks with pilots on a package covering a range of topics from pay, pensions and working conditions broke down earlier this year and the two sides instead agreed to discuss topics individually.

(Reporting by Victoria Bryan and Peter Maushagen; Editing by Tina Bellon and Jane Merriman)