MILAN, Jan 31 (Reuters) - Italian investment fund FSI said on Monday it would take a 60% stake in the payment activities of Italian cooperative bank Iccrea Banca in a 500 million euro ($560 million) deal, after a spate of acquisitions in Italy's payment sector.

Electronic payments are catching on rapidly in Italy, but are still below the European average, with cash widely used and Italy's Nexi last year finalised a tie up with smaller rival SIA to form one of Europe's largest payment groups.

FSI and Iccrea said in a joint statement they had signed an agreement to develop BCC Pay, which gathers Iccrea's merchant acquiring activities and at present only offers its services to Iccrea group branches.

Iccrea will retain a 40% in the new company and the deal is expected to be concluded by summer 2022, they added.

"We believe the payment sector can grow fast," FSI Chief Executive Maurizio Tamagnini told a press briefing.

BCC Pay, which has 4 million payment cards, will be able to offer new services and products to Iccrea clients but also to other banks, especially small and medium ones, he said.

"The new company has no debt, so if opportunities arise, BCC Pay will be able to acquire companies in the banking sector to diversify its customer base and increase its size," he added.

FSI has recently reinvested in Italian banking software provider Cedacri, alongside financial data and technology firm ION Group. It also acquired a stake in Italian IT consulting firm Lynx.

Tamagnini said that FSI is a medium-long term investor in BCC Pay, but it is not planning to create a financial services hub with Lynx or Cedacri.

It does not rule out the entrance of other shareholder or the possibility of a listing in the future, he added. ($1 = 0.8923 euros) (Reporting by Elisa Anzolin, writing by Giulia Segreti; editing by Agnieszka Flak and Alexander Smith)