By Kevin Buckland

TOKYO (Reuters) - Most Asia-Pacific stock markets rose on Thursday amid receding bets for a U.S. rate hike this month and relief over the passage of the U.S. debt ceiling bill through the House.

The dollar sagged to a one-week low versus the yen and hung close to Wednesday's more-than-two-month trough to the euro after Federal Reserve officials including Governor and vice chair nominee Philip Jefferson pointed to a rate hike "skip" at the June 13-14 policy meeting.

Treasury yields rose slightly from nearly two-week lows.

Crude oil prices edged off four-week lows following a surprise swing back to growth in a private survey of Chinese factory activity, with an OPEC+ meeting looming on the weekend.

MSCI's broadest index of Asia-Pacific shares gained 0.45%, rebounding after touching the lowest level since March 22 in the previous session.

Japan's Nikkei added 0.29%, while Hong Kong's Hang Seng gained 0.5% and mainland Chinese blue chips advanced 0.53%.

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.

"This has gone through with a very big majority, so there's enough bipartisan support that 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 (OTC:NABZY).

""What this does is it turns the attention to the incoming data and the Fed meeting this month," Attrill added.

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

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 is inclined to support a "skip" in rate hikes.

The dollar was little changed at 139.435 yen after slipping to the lowest since May 25 at 138.96 earlier in the session.

The euro was flat at $1.06905. It sank as low as $1.0635 on Wednesday for the first time since March 20.

Benchmark 10-year U.S. Treasury yields edged up to 3.6655% in Tokyo, after dipping to 3.6140% overnight for the first time since May 18.

Brent crude futures for August delivery rose 46 cents, or 0.63% to $73.06 a barrel, while U.S. West Texas Intermediate crude (WTI) added 40 cents, or 0.59%, to $68.49 a barrel.