By Kevin Buckland and Rae Wee

TOKYO, July 12 (Reuters) - The U.S. dollar hit a fresh two-decade peak versus major peers on Tuesday, hoisted by safety bids and expectations of further aggressive rate hikes by the Federal Reserve, while the euro was pinned close to a 20-year low near parity to the greenback.

The dollar index, a measure against six counterparts, with the euro most heavily weighted, was 0.25% higher at 108.43. It had earlier climbed to 108.47, its highest since October 2002.

"Haven demand for USD, coupled with an upside surprise in last Friday’s payrolls release, likely contributed to the latest bout of dollar strength," said analysts at Maybank.

That dollar bullishness was showcased across much of the currency markets, with the euro falling as low as $1.0006 on Tuesday, the weakest since December 2002. It last changed hands down 0.29% at $1.0013.

Sterling was similarly down 0.25% to $1.18645, after earlier sinking to a fresh two-year low at $1.186.

"EUR depreciation of late appears to have been largely driven by the market reassessing the potential for a more significant growth downturn in the Euro area, amplified by energy woes, war dragging on longer than expected and doubts over ECB's anti-fragmentation tool," the Maybank analysts said.

The biggest single pipeline carrying Russian gas to Germany, the Nord Stream 1 pipeline, began annual maintenance on Monday, with flows expected to stop for 10 days.

Governments, markets and companies are worried Russia might extend the shutdown because of the war in Ukraine, exacerbating the continent's energy supply crunch and potentially speeding a recession.

"All eyes will just be on whether Russian gas flows will return via the Nord Stream 1 pipeline following the end of maintenance next week," said Carol Kong, a currency strategist at Commonwealth Bank of Australia.

"But in the meantime, I think concerns about a potential shut off of Russian gas flows will continue to keep the euro/ dollar heavy and that would in turn mean the dollar will keep strengthening."

Euro weakness has been a big part of the dollar index's push higher, with the safe-haven U.S. currency also supported by worries about growth elsewhere too, with China in particular implementing strict zero-COVID policies to contain fresh outbreaks.

Arguably the biggest factor in the dollar's rise, however, is the view the Fed will hike rates faster and further than peers.

The Fed is expected to lift rates by 75 basis points for a second straight time at its July 26-27 meeting. Fed funds futures are pricing for its benchmark rates to rise to 3.50% by March, from 1.58% currently.