MUMBAI, Dec 6 (Reuters) - The Indian rupee extended its opening decline against the dollar on Tuesday, to slip to its lowest level in over a month and below a key level.

The rupee was at 82.30 to the U.S. dollar by 9.30 a.m. IST, down from 81.79 in the previous session. The local unit opened at 81.9350 before swiftly falling below the 50-day moving average of 81.98 and the psychological level of 82.

There was probably another round of stop losses triggered once USD/INR moved about 82, a trader said, recalling a possible dividend dollar outflow of a mining company. However, they added "it was difficult to be sure".

"It could be that the news is chasing the price action."

The trader requested anonymity as they are not allowed to speak to the media.

The rupee's weakness was fuelled by the broad decline in Asian currencies after better-than-expected U.S. data brought back the focus on how high U.S. rates will rise in the current cycle. Treasury yields rose overnight and U.S. equities tumbled.

U.S. services industry activity unexpectedly picked up in November. The Institute for Supply Management(ISM) said on Monday its non-manufacturing PMI (Purchasing Managers' Index) increased to 56.5 last month from 54.4 in October.

"With no Fed official citing a smaller 50 basis points hike next week, markets were vulnerable to better-than-expected U.S. data," DBS said in a note.

The dollar index was at 105.28, having reached near 104 at one point on Monday. Asian equities were mostly lower. (Reporting by Nimesh Vora; Editing by Janane Venkatraman)