* Yields hold at higher levels after payrolls report * Treasury to sell $72 bln in new 3, 10, 30-year debt * Fed buys $3.31 bln in debt due 2020-2023 By Karen Brettell NEW YORK, May 6 (Reuters) - U.S. Treasuries prices slipped slightly on Monday as investors continued to digest Friday's better than expected jobs report, which sent yields surging to their highest levels in three weeks. The U.S. government bonds are expected to stay at the relatively higher yields as investors prepare for $72 billion in new supply this week, with the recent selloff also seen as likely helping demand as investors take advantage of the yield backup. Friday's jobs gains caught traders offside, as most were anticipating a gloomier jobs picture after other economic releases pointed towards more sluggish growth. "There was a significant amount of buying and short covering and capitulation around month-end and prior to that number, with expectations having been lowered substantially going in," said Dan Mulholland, managing director in Treasuries trading at BNY Mellon in New York. The positive jobs surprise, with employers adding 165,000 jobs in April and the jobless rate falling to 7.5 percent, the lowest since December 2008, left traders scrambling to cover long exposures and sent yields surging. Benchmark 10-year Treasuries yielded 1.75 percent on Monday, up from 1.74 percent on Friday and up from 1.62 percent before the jobs data was released. Thirty-year bonds yielded 2.97 percent on Monday, up from 2.96 percent late on Friday and up from 2.82 percent before the jobs report. Despite Friday's jobs gains, many economic analysts believe that economic growth is still too slow and investors have pared back expectations that the Federal Reserve may taper or end bond purchases this year as inflation also dips. That may hold yields down near historic lows for some time yet. Data last week showed that the Fed's preferred gauge of consumer prices, the personal consumption index, slowed to 1.0 percent in March from 1.3 percent in February, the smallest gain in three and a half years. Market inflation expectations as measured by forward contracts that show where traders think five-year inflation will be in five-years time, also a closely watched indicator by the Fed, have also slipped. The contracts now show expectations of 2.77 percent, down from around 3 percent at the beginning of the year. "It's possible that the Fed starts to focus on inflation as a reason to extend QE, rather than unemployment," said Carl Lantz, head of U.S. interest rate strategy at Credit Suisse in New York. The Federal Reserve said on Wednesday it may increase or decrease bond purchase from its current $85 billion per month, depending on the strength of the economy and on inflation, though most see the Fed as more likely to continue purchases for longer. Before the recent slowdown in data most economists had expected the Fed would taper buying this year, and end purchases at the end of the year. The Fed bought $3.31 billion in notes due 2020 to 2023 on Monday as part of this program and will purchase between $1.25 billion and $1.75 billion in bonds due 3026 to 2043 on Tuesday. The relatively higher yields, meanwhile, are expected to help the Treasury sell $32 billion in three-year notes on Tuesday, $24 billion in 10-year notes on Wednesday and $16 billion in 30-year bonds on Thursday. "The higher yields will entice some buying," said Lantz.