MUMBAI - The Indian rupee opened lower versus the U.S. currency on Monday and fell further as foreign banks snapped up the dollar, likely for their custodial clients, traders said.

The rupee was trading at 81.80 per U.S. dollar by 0954 GMT, down from 81.34 in the previous session. The local unit had opened at 81.62.

Foreign banks were primarily responsible for the rupee's drop since the open as they were likely mopping up dollars for their overseas custodial clients, traders said.

Overseas investors have turned net sellers of Indian equities recently—having withdrawn about $2.5 billion over the last seven trading sessions–likely fuelled by mounting concerns over the economic outlook in the U.S. and other developed nations.

The further rise in Treasury yields and the volatility in U.K. assets have also weighed on demand for risk assets.

This suggests that now the rupee will not have the support of equity inflows like it did in August and the first half of September. The rupee is not too far away from the record low of 81.95 reached last week.

Asian currencies declined on the day, and the dollar index was a tad higher at 112.28.

Indian shares slipped to begin the week, but as has been the case more often than not, the decline was smaller relative to most other Asian gauges and U.S. equities.

The rupee and Indian equities were pressured by the rise in oil prices, with Brent crude December contracts advancing 2.6% to $87.36, recovering from the near 10% drop last month.

To support prices, the Organization of the Petroleum Exporting Countries and their allies, are considering an output cut of 0.5 million to 1 million bpd ahead of Wednesday's meeting, OPEC+ sources told Reuters.

U.S. ISM manufacturing data is due later in the day, while the important monthly jobs report is due Friday.

(Reporting by Nimesh Vora; Editing by Savio D'Souza)