* Latest 30-year bond supply seen at lowest yield since June
* Most Treasuries yields hold steady near three-week lows
* U.S. weekly jobless claims near seven-year trough
* Fed to buy $2.75-$3.50 billion debt that matures in 2018
NEW YORK, April 10 (Reuters) - U.S. Treasuries prices rose modestly on Thursday before a $13 billion auction of 30-year bonds after market-friendly minutes from the Federal Reserve's March policy meeting spurred a rally in short-to-medium notes, sending yields to three-week lows.
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, analysts and traders said.
Longer-dated Treasuries, while they lagged shorter maturities on Wednesday, have grown more expensive after a mildly disappointing March jobs report last week. This might pinch demand for them as traders expect the upcoming 30-year bond supply to sell at the lowest yield in 10 months.
"The Fed basically went out of its way to say we are not going to raise rates any time soon. This makes 30-year bond a tough sell at this level," said Mike Cullinane, head of Treasuries trading at D.A. Davidson & Co. in St. Petersburg, Florida.
The Treasury Department will sell a 30-year bond issue at 1:00 p.m. EDT (1700 GMT) that was originally introduced in February.
Bidding for this week's coupon supply has been uneven with solid appetite for Tuesday's $30 billion in three-year debt and tepid demand for Wednesday's $21 billion in 10-year notes.
Large fund managers and other direct bidders have again been a wild card. They bought nearly 24 percent of the three-year supply, their biggest share in 14 months, while they accounted for 15 percent of the purchases at the 10-year auction, which was their smallest share since January, Treasury data showed.
In "when-issued" activity, traders expected the 30-year auction to fetch a yield of 3.563 percent, which would be lowest since the 30-year auction in June 2013.
On the open market, the benchmark 10-year note last traded up 3/32 in price to yield 2.674 percent, down 1 basis points from late on Wednesday.
Two-year notes were steady for a yield of 0.367 percent, while five-year debt was up 3/32 in price with a yield of 1.617 percent, down 2 basis points on the day.
Treasuries prices briefly turned flat after news jobless claims fell to their lowest weekly level since May 2007, signaling more improvement in the jobs sector.
The Fed was scheduled to buy $2.75 billion to $3.50 billion in Treasuries due in 2018 at 11:00 a.m. (1500 GMT), which is part of its intended $30 billion Treasuries purchases in April.
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 interpreted to indicate the central bank might raise 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.
Late Wednesday, Fed Governor Daniel Tarullo said at an event in Washington, "We are well advised to proceed pragmatically."
Chicago Fed President Charles Evans, who is not an FOMC voter this year, will speak at 11:30 a.m. (1530 GMT) in a panel on global monetary policy in Washington.
(Reporting by Richard Leong; Editing by Bernadette Baum)