MUMBAI, July 8 (Reuters) - The Indian rupee was mildly stronger on Monday, tracking a rise in its Asian peers, which were aided by a decline in U.S. bond yields after fresh economic data boosted hopes of rate cuts by the Federal Reserve later this year.

The rupee was at 83.44 against the U.S. dollar as of 10:15 a.m. IST, up slightly from its close at 83.4850 in the previous session.

U.S. Treasury yields and the dollar declined after data on Friday showed that the unemployment rate rose to 4.1% in the United States, while annual wages increased at the slowest pace in three years, pointing to a slackening of the labour market.

The data follows a string of economic indicators that pointed to a cooling of the U.S. economy, which has helped push up the odds of a September rate cut by the Fed to nearly 76%, from about 64% a week earlier, according to CME's FedWatch tool.

"Asian FX took a breather on the back of broad US dollar weakness ... the risk for Asian currencies, though, remains skewed to the downside, with the Fed staying patient," Lloyd Chan, senior currency analyst at MUFG Bank, said in a note.

Asian currencies were under pressure last week, with the Japanese yen falling to its lowest in 38 years, while the offshore Chinese yuan touched its weakest level since November.

Fed policymakers have largely maintained a wait-and-see stance on the future path of interest rates despite recent weakness in U.S. economic data.

Asian currencies were mostly higher on the day, while the dollar index was at 104.9 after falling 0.2% on Friday.

Traders expect the rupee to continue seeing mostly sideways price action between 83.40 and 83.55. (Reporting by Jaspreet Kalra; Editing by Sonia Cheema)