TREASURIES-Steady to firmer, eyes on stocks and JGBs

*Rate rise expectations ebb due to weak U.S. equities

*Investors await Thursday's U.S. jobs data and ECB decision

*Treasuries could dip if Trichet fans rate rise jitters

By Masayuki Kitano

TOKYO, July 2 (Reuters) - U.S. Treasuries were steady to firmer in Asian trading on Wednesday, supported by some weakness in regional stock markets and gains in Japanese government bonds.

Treasuries have rallied since mid-June as investors scaled back expectations for the scope of possible monetary tightening by the Federal Reserve later this year, due to concerns about the U.S. economy's outlook.

Treasuries have been supported by such worries, highlighted by the S&P 500's 8.6 percent fall in June and renewed concerns about financial institutions' losses from the credit market turmoil.

"Equities have fallen pretty far, led by financial shares," said a portfolio manager for a Japanese insurer.

"Even if the jobs data comes in somewhat strong, the market probably will not go back to pricing in three interest rate hikes later this year," he said.

U.S. short-term interest rate futures are now pricing in a federal funds rate of around 2.4 percent by year-end, up from 2.0 percent now. At one point in June, rate futures had priced in a fed funds rate of 2.75 percent by the end of the year FEDWATCH.

The benchmark 10-year Treasury note rose 3/32 in price to yield 3.996 percent US10YT=RR, down 1 basis point from late U.S. trading on Tuesday.

The two-year note was steady in price with a yield of 2.660 percent US2YT=RR, little changed from late New York.

In the stock market, Tokyo shares fell around 1 percent .N225 and South Korean equities dropped over 2 percent .

Japanese government bonds edged higher and the 10-year JGB yield dipped 1.5 basis points to 1.655 percent JP10YTN=JBTC.

Investors were awaiting Thursday's key events, namely the U.S. jobs data and the European Central Bank's rate decision.

The ECB is seen likely to raise interest rates by 25 basis points to 4.25 percent at its policy meeting on Thursday, and the focus will be on whether ECB President Jean-Claude Trichet drops any hints about the possibility of further rate increases.

"It seems that there is a lot of focus on the ECB," the portfolio manager said, adding that Treasuries were likely to take a hit if Trichet stokes jitters about further rate increases by the ECB beyond the expected rate rise this week. (Editing by Chris Gallagher)