TREASURIES-Steady to firmer as rate rise expectations ebb

*Gains tempered by firmness in Asian equities

*Tough quarter for Treasuries drawing to a close

By Masayuki Kitano

TOKYO, June 30 (Reuters) - U.S. Treasuries were mostly steady to firmer on Monday, drawing support from receding market expectations for Federal Reserve interest rate increases later this year.

Treasuries have rallied over the past couple of weeks as investors scaled back market expectations for the timing and scope of possible monetary tightening by the Fed in coming months.

This trend seems likely to remain intact in the near term unless the U.S. jobs data due on Thursday turns out to be surprisingly strong, and causes Fed rate hike expectations to rise again, said a senior trader for a European investment bank.

"The market has priced in Fed tightening and that's just wrong. That's starting to be taken out of the market," the trader said, adding that the Fed was likely to keep interest rates on hold until it sees more economic data.

The benchmark 10-year Treasury note inched up 2/32 in price to yield 3.959 percent US10YT=RR, down 1 basis point from late U.S. trading on Friday.

The two-year note, the sector most sensitive to changes in the outlook for monetary policy, was steady in price for a yield of 2.625 percent US2YT=RR, steady from late U.S. trade.

Gains in Treasuries were limited by the firmness of Asian equities, said the European investment bank trader.

Japan's Nikkei share average rose 0.3 percent .N225, while Hong Kong's Hang Seng Index rose around 0.1 percent .HSI.

Despite their rally over the past two weeks, the April-June quarter has been a tough three months for Treasuries.

The two-year yield has jumped nearly 100 basis points since the end of March, as surging oil prices and tough anti-inflation talk from Fed officials bolstered market expectations for the central bank to raise interest rates a few times later this year.

U.S. short-term interest rate futures are fully pricing in a Fed rate hike to 2.25 percent by the Fed's policy meeting in October, and futures imply a federal funds rate of roughly 2.40 percent by year-end, up from 2.00 percent now. FEDWATCH

Still, the implied probabilities for rate increases by year-end are far below levels earlier in June, when a series of hawkish remarks from Fed officials had the market looking for at least 75 basis points in tightening. (Editing by Chris Gallagher)