By Kevin Buckland

TOKYO, Aug 1 (Reuters) - The dollar hung near a three-week low to major peers on Monday as markets continued to wager that the Federal Reserve has less tightening to do with the U.S. economy at risk of recession.

The dollar index, which measures the currency against six counterparts, edged 0.1% lower to 105.89, slipping back toward Friday's low of 105.53, a level not seen since July 5.

Data at the end of last week tossed the greenback in both directions, rising initially after the personal consumption expenditures (PCE) price index showed the fastest inflation since 2005, only to sink after the final University of Michigan report - closely watched by Fed policymakers - showed slipping consumer inflation expectations.

The big economic focus for this week will be the monthly U.S. jobs report on Friday.

Traders currently price about 31% probability that the Fed will keep its current 75 basis-point pace of rate hikes at its next meeting on Sept. 21, with 69% odds for a smaller half point increase.

"Markets look to be betting the Fed has done the lion's share of its task on inflation and will be receptive to slowing activity data," Taylor Nugent, a markets economist at NAB in Sydney, wrote in a client note.

The dollar slipped 0.22% to 132.925 yen, heading back toward the six-week low of 132.505 reached on Friday.

The currency pair is extremely sensitive to changes in U.S. long-term Treasury yields, with the benchmark 10-year hovering around 2.67% after sliding to the lowest since early April at 2.618% at the end of last week.

The euro, however, edged 0.07% lower to $1.0218, continuing its consolidation near the middle of its range over the past week and a half.

Sterling was about flat at $1.2186, after hitting the highest since June 28 at $1.2245 on Friday. Markets are laying 67% odds for a half-point rate hike on Thursday, compared to 33% probability of a quarter-point increase.

The Reserve Bank of Australia sets policy on Tuesday, and is expected to deliver another half point increase, with traders seeing just a 16% chance of a smaller quarter point tightening.

The Aussie dollar slipped 0.19% to $0.69775 on Monday, but after touching a six-week high of $0.7032 in the previous session.

"Should the market continue to hear what it wants from the Fed, the Aussie can readily spend more time above $0.70," NAB's Nugent said.

"But $0.65-0.70 is still seen containing most of the price action in coming months."

(Reporting by Kevin Buckland; Editing by Simon Cameron-Moore)