MUMBAI, July 9 (Reuters) - The Indian rupee was largely flat in early trading on Tuesday as mild dollar sales from state-run banks supported the currency even as most of its Asian peers slipped.

The rupee was at 83.4775 against the U.S. dollar as of 10:10 a.m. IST, barely changed from its previous close at 83.4925.

Most Asian currencies edged lower ahead of Federal Reserve Chair Jerome Powell's closely watched two-day testimony before Congress starting later in the day. The dollar index was at 105 after rising 0.1% on Monday.

Powell's remarks will follow a string of relatively soft U.S. economic data which has helped push up the odds of a September rate cut by the Fed to above 75%, according to the CME's FedWatch tool.

"If Powell hints that the Fed is closer to an interest rate cut in September, it could send the (dollar index) below 104.75, a critical support level," DBS Bank said in a Tuesday note.

However, traders do not expect Powell's remarks to have a notable impact on the rupee.

It is "tricky to say" which cue may move the currency out of the prevailing 83.40-83.60 band, with the Reserve Bank of India expected to limit depreciation, while corporate dollar demand caps gains, a foreign exchange trader at a state-run bank said.

Inflows worth about $2.1 billion into Indian debt and equities over July so far, according to stock depository data, have also supported the rupee.

Mostly range-bound price action though has squeezed volatility expectations on the dollar-rupee pair with the 1-month implied volatility dropping to 1.75%, its lowest since March.

Alongside Powell's testimony, remarks from other Fed speakers will also be in focus heading into the U.S. consumer inflation print on Thursday. (Reporting by Jaspreet Kalra; Editing by Sohini Goswami)