LONDON (Reuters) - Reinsurance rates have softened in the June/July renewals season, against a backdrop of overcapacity, although the pace of the price reductions has slowed, a report by broker Willis Re on Friday showed.

Reinsurers, which take on a portion of an insurer's risk and help to pay for large claims in exchange for part of the premium, have seen competition rise sharply as more funds look to compete on deals in response to low interest rates in more traditional markets.

Some resinsurers have removed capacity given the low pricing, but there is no indication yet it has been enough to stabilize the market, Willis Re said in its latest 1st View Renewals report.

"Capacity remains abundant and continues to overhang the market in virtually all classes and regions," John Cavanagh, Global CEO of Willis Re, said.

So far in 2016, just one major catastrophe loss – the Fort McMurray fires in Canada – will produce any meaningful catastrophe claims for reinsurers, he said.

"Any relief that pricing may be nearing the bottom of the cycle is counterbalanced by concern over how and when rates might start to increase, even modestly, on a wider basis," Cavanagh said. "The alternative is a market that faces a number of years bumping along at current levels earning very modest returns."

Willis Re is the reinsurance business of global advisory and broking company Willis Towers Watson <WLTO.O>.

On the issue of Britain's vote to leave the European Union, Cavanagh said the industry was well-placed to cope.

"Underpinned by the strong customer-centric regulation in the UK and EU, we do not see any material risk to clients generally in terms of reinsurers' ability in the immediate future to offer continuity in the supply of reinsurance capital and consistency of approach," he wrote in the report.

(Reporting by Simon Jessop. Editing by Jane Merriman)