SYDNEY, June 13 (Reuters) - The Australian and New Zealand dollars edged cautiously higher on Tuesday, after the U.S. dollar and short-term Treasury yields dipped ahead of inflation data that could make or break the case for a Federal Reserve rate pause this week.

The Aussie rose 0.2% to $0.6762, having hit a fresh one-month top of $0.6774 on Friday. That remained the near-term resistance, while major support lies at the 200-day moving average of $0.6689.

The kiwi dollar climbed 0.1% higher to $0.6130, after touching a three-week high of $0.6153 on Friday. Resistance is about $0.6150, while it has support at the 21-day moving average of $0.6125.

The two stole a march higher after the U.S. dollar slipped a little in Asia on expectations of a pause in the Fed's interest rate hike cycle on Wednesday.

The U.S. inflation report due later on Tuesday is expected to show a welcome cooling in consumer inflation in May, with headline inflation easing to an annual rate of 4.1% from April's 4.9%, a result that would add to the case for a Fed pause.

Markets are currently pricing in an 80% chance that the Fed will keep rates on hold at this week's meeting.

Earlier in the day, soft survey readings on Australian businesses and consumers and China's move to cut a key short-term rate had weighed on the Aussie.

"The Aussie suffered a few wobbles in its 'witching hour' when Australian data releases overlapped with early China trade," said Sean Callow, a senior currency strategist at Westpac.

The Aussie slipped under 0.6740 as the yuan weakened on the People's Bank of China reverse repo cut, but later recovered as the U.S. dollar lost ground, he said.

Australia's government bond yields were lower on Tuesday. The benchmark 10-year yields fell 5 basis points (bps) to 3.910% while three-year yields slipped 1 bps to 3.838%. (Reporting by Stella Qiu; Editing by Jamie Freed)