NEW YORK, May 6 (Reuters) - U.S. crude oil futures rose more than $1 on Wednesday following a report of slowing private sector job losses in April which also caused the dollar to weaken against the euro.

Oil markets awaited a government inventory report due later this morning.

On the New York Mercantile Exchange at 8:50 a.m. EDT (1350 GMT), June crude CLM9 was up $1.06, or 1.97 percent, at $54.50 a barrel, trading from $53.57 to $55.96, a fresh 2009 peak which eclipsed the $54.83 high set Tuesday. (Reporting by Robert Gibbons; Editing by John Picinich)