* Benchmark yields fall to lowest level in about four weeks
* FOMC minutes underpin bids for bonds, stock loss adds demand
* Latest 30-year bond supply fetches lowest yield since June
* U.S. weekly jobless claims near seven-year low (Updates market action, adds quotes)
NEW YORK, April 10 (Reuters) - The U.S. Treasuries market rallied on Thursday with benchmark yields falling to their lowest in nearly four weeks as market-friendly minutes from the Federal Reserve's March policy meeting renewed appetite for government debt.
A steep selloff on Wall Street, where the major indexes lost between 1 and 3 percent, ramped up safe-haven bids for Treasuries and stoked demand at a $13 billion 30-year bond auction that fetched the lowest yield in 10 months.
The latest Federal Open Market Committee minutes, released on Wednesday, suggested most policy-makers wanted to cling to a near-zero rate policy they adopted in December 2008 until the U.S. economy creates more jobs and an inflation rate that achieves its 2 percent target, investors said.
"(The minutes) were very dovish. We are going to see low rates in the foreseeable future," said Jill King, senior portfolio manager at Horizon Cash Management LLC in Chicago.
It was longer-dated Treasuries' turn to shine a day after they lagged shorter maturities that gained on the FOMC minutes, which propelled their yields to three-week lows.
Bond yields in general pushed passed some key chart levels on Thursday, portending further decline, analysts said.
Longer-dated debt generated higher total returns than intermediate issues despite similar yield declines.
Benchmark 10-year Treasuries notes were up 17/32 in price with a yield of 2.625 percent, down 6 basis points from late on Wednesday.
The 30-year bond jumped 1-6/32 point in price with its yield at 3.501 percent, down 6 basis points. That was its biggest one-day yield decline in nearly four weeks.
The seven-year Treasuries yield was 7 basis points lower at 2.160 percent.
On a total return basis, the 10-year note and 30-year bond were on track to earn 0.59 percent and 1.33 percent in late trading, respectively, according to Reuters data. This compared with the seven-year note which was expected to generate a 0.47 percent return on the day.
The intense bids for U.S. government debt seeped into the 30-year bond sale, the last leg of this week's $64 billion in coupon-bearing supply.
"It was pretty decent auction," said Aaron Kohli, interest rate strategist at BNP Paribas in New York.
Treasuries' strong performance was part of a banner day in the global bond market whose highlight was Greece's first debt sale two years after it defaulted.
U.S. stocks, in contrast, suffered heavy losses with the Nasdaq on track for its worst day since June 2012.
"That's brought a bid into Treasuries. Longer-term yields could come down a little more," said Dan Heckman, senior fixed income strategist at U.S. Bank Wealth Management in Kansas City, Missouri.
Treasuries prices briefly turned flat earlier after news jobless claims fell to their lowest weekly level since May 2007, signaling more improvement in the jobs sector.
FOMC MINUTES EASE RATE-HIKE WORRIES
Disclosure of the FOMC's discussion over its bias to keep rates low mitigated earlier fears stemming from the Fed's summary of economic projections (SEP), which some traders took as a sign the central bank might raise rates earlier and at a faster pace than they had thought.
Compounding the perceived hawkish view on rates were remarks by Fed Chair Janet Yellen at a press conference after the March policy meeting, when she said the Fed might increase rates a "considerable time" after it completed its bond-purchase program, a period she defined as "around six months."
Traders dumped short-to-medium Treasuries in reaction to policy-makers' rate views and Yellen's remarks, resulting in the worst day for the five-year notes since July.
Since the March policy meeting, top Fed officials have downplayed Yellen's "six month" reference and the importance of the "dots" or the graphical presentation of SEP.
Chicago Fed President Charles Evans, who is not an FOMC voter this year, said in a panel on global monetary policy in Washington that easy monetary policy is needed in the United States and around the world. (Reporting by Richard Leong; Editing by Bernadette Baum and Meredith Mazzilli)