By Tom Wilson

LONDON, June 1 (Reuters) -Global shares rose on Thursday as traders pared back expectations of a U.S. rate hike this month and were relieved by the passage through the U.S. House of Representatives of a bill to suspend the federal debt ceiling.

A divided House passed a bill to suspend the $31.4 trillion debt ceiling - and avert a catastrophic default - with majority support from both Democrats and Republicans, stoking optimism that it can move through the Senate before the weekend.

The pan-European STOXX 600 index .STOXX rose 0.8% after closing at a two-month low in the previous session. U.S. S&P 500 e-Mini futures EScv1 were 0.3% higher.

The U.S. legislation in essence temporarily removes the federal government's borrowing limit through Jan. 1, 2025. The timeline allows President Joe Biden and Congress to set aside the politically risky issue until after the November 2024 presidential election.

"It's very hard to believe this isn't going to be even more of a formality in the Senate," said Ray Attrill, head of foreign exchange strategy at National Australia Bank.

The MSCI world equity index .MIWD00000PUS, which tracks shares in almost 50 countries, added 0.3%.

Also bolstering the mood were U.S. Federal Reserve officials including governor and vice chair nominee Philip Jefferson pointing to a rate hike "skip" at the Fed's June 13-14 policy meeting. The comments saw the dollar dip to a one-week low versus the yen JPY=EBS before it added 0.2%, while Treasury yields edged up from nearly two-week lows.

"The market at the moment is also really focused on broad macro trends, such as options for tapers by central banks," said Sandrine Perret, a portfolio manager at Unigestion. "We are not there yet, but closer to it."

Earlier, MSCI's broadest index of Asia-Pacific shares .MIAP00000PUS gained as much as 0.8% before giving up about half of its gains, rebounding after touching the lowest level since March 22 in the previous session.

A surprise swing to growth for Chinese factory activity had also provided a lift to sentiment, in a rare recent positive sign for the country's post-pandemic recovery.

HIKE SKIP?

Money markets currently lay about 38% odds for a hike from the Fed on June 14, swinging back from about 70% earlier on Wednesday, after some unexpectedly hot jobs numbers. FEDWATCH

However, shortly after, the Fed's Jefferson said skipping a rate hike in two weeks would provide policymakers time to see more data before making a decision. Philadelphia Fed President Patrick Harker also said on Wednesday that for now he was inclined to support a "skip" in rate hikes.

More closely watched employment data is due this week, with the ADP survey out later in the day, followed by the monthly non-farm payrolls report on Friday.

"It's been a fairly strong retracement in terms of the market's expectations for the June meeting, and it's come contrary to the data," said Tony Sycamore, an analyst at IG Markets.

The euro EUR=EBS steadied on Thursday near a two-month low after data showed euro zone inflation eased more than expected last month. The euro EUR=EBS flattened at $1.0690, towards Wednesday's two-month low of $1.0635.

Benchmark 10-year U.S. Treasury yields US10YT=RR edged up to 3.6829%, after dipping to 3.6140% overnight for the first time since May 18.

Reporting by Tom Wilson in London; additional reporting by Kevin Buckland in Tokyo; Editing by Emelia Sithole-Matarise and Mark Potter

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