* Sterling struggles, down more than 7 pct in June on Brexit

* Dollar slips more than 7 pct in June vs perceived safe-haven yen

By Lisa Twaronite

TOKYO, June 30 (Reuters) - The dollar took a breather in Asia on Thursday but remained near a 3-1/2-month high against a basket of currencies hit in the wake of Britain's stunning vote to exit from the European Union, while the battered sterling continued to struggle.

The dollar index, which tracks the greenback against a basket of six major rivals, edged up 0.1 percent to 95.836 , on track for a monthly loss of 0.1 percent.

While the U.S. currency mostly benefited from the massive wave of risk aversion that crashed over global markets after the Brexit vote, fading expectations of a U.S. interest rates this year have stolen some of its thunder.

Interest rate futures suggested traders saw the Fed holding policy steady - or even cutting rates - through at least early 2018.

The dollar index rose as high as 96.705 on Monday, when the pound plumbed 31-year lows after the results of the UK vote on Friday.

Sterling was down 0.2 percent at $1.3395, well above Monday's nadir of $1.3122 but still poised to lose more than 7 percent for the month.

Sterling "has come a long way, and there is still a lot of uncertainty," said Sue Trinh, senior currency strategist at RBC Capital Markets in Hong Kong.

"We've got month-end shenanigans as well, with some fund managers rebalancing their hedges, so that could also add to the volatility today," she said.

The euro was nearly flat against the pound at 82.85 pence edging away from Monday's high of 83.80, which was its loftiest peak in over than two years.

"The odds may be against them but investors are hoping that the worst is over for currencies and equities and the gaps on Friday will be filled," Kathy Lien, managing director of foreign exchange strategy at BK Asset Management, wrote in a note to clients.

"But considering there's been had no additional clarity on the terms of Brexit or the outlook for the UK economy and global economy since Britain's decision to leave the European Union on Friday, we don't see fundamental support for the recent moves," she said.

Chaos also continued in Britain's political arena, as both main opposition Labour Party and ruling Conservative Party headed for leadership battles.

Japan's foreign ministry said Prime Minister Shinzo Abe would have separate phone talks with British Prime Minister David Cameron and German Chancellor Angela Merkel later on Thursday.

The euro remained under pressure, down 0.2 percent at $1.1101, but remained well above its 3 1/2-month low of $1.0912 hit on Friday last week. It was down 0.3 percent for the month.