* Dollar index inches away from recent 5-week low
* Aussie slides on comments by RBA's Stevens
* Big central bank meetings, U.S. jobs data due this week
By Masayuki Kitano
SINGAPORE, July 30 (Reuters) - The dollar inched higher against a basket of major currencies on Tuesday, while the Australian dollar slid after Australia's central bank governor said it could fall further and there was room for more interest rate cuts.
The comments by Reserve Bank of Australia (RBA) Governor Glenn Stevens were taken by investors as affirming expectations for a rate cut at the RBA's meeting next week and added to downward pressure on the Aussie dollar.
The Australian dollar fell 1.5 percent on the day to $0.9069 . The Aussie dollar had already been on the back foot ahead of the comments by Stevens, dented by weaker-than-expected Australian building approvals data.
The slide in the Australian dollar helped lend broad support to the U.S. dollar.
The greenback inched up 0.1 percent versus a basket of major currencies to 81.777, edging away from a five-week trough of 81.499 reached on Monday.
"I think the Aussie dollar is running things right now - U.S. dollar strength across the board on the Stevens remarks," said a U.S.-based FX trader.
The dollar edged up 0.3 percent against the yen to about 98.30 yen.
The euro eased 0.1 percent to $1.3256, staying below a five-week high near $1.3297 set Friday on trading platform EBS and chart resistance at $1.3300.
Investors are focusing on major events later this week for clues to the market's direction, including the U.S. Federal Reserve's two-day policy meeting that starts later on Tuesday.
The dollar has retreated over the past few weeks after Federal Reserve Chairman Ben Bernanke stressed in a series of comments that a highly accommodative monetary policy is needed for the foreseeable future and that any reduction in the Fed's bond purchases is not set in stone.
The greenback also came under pressure after a Wall Street Journal report last week said the Fed may debate changing its forward guidance to help hammer home the message it will keep interest rates low for a long time to come.
Sim Moh Siong, FX strategist for Bank of Singapore, played down the chances of the Fed announcing such changes at this week's policy meeting, which will not be followed by a post-meeting news conference by Bernanke.
"The likelihood of that may not be high, since there is no press conference," Sim said. The next Fed meeting with a scheduled news conference by the Fed chairman takes place in September.
In addition to the Fed, the European Central Bank and the Bank of England also hold policy reviews this week.
Investors are also waiting for second quarter U.S. growth data due on Wednesday and the influential U.S. jobs report for July on Friday.
Source: Flash Chart Teletrader Software AG
Chart: WorldWideMarkets Flash Trader