WRAPUP 2-Rice flies to India to ease tension with Pakistan

* Rice flies to India for talks on Mumbai

* India demands most-wanted fugitives from Pakistan

* Pakistan offers joint investigation

By C. Bryson Hull

NEW DELHI, Dec 3 (Reuters) - U.S. Secretary of State Condoleezza Rice flew to New Delhi on Tuesday hoping to ease tension between India and Pakistan that has surged over the Mumbai attacks and put at risk U.S. counterterrorism efforts in the region.

The three-day rampage by 10 Islamist gunmen in India's financial capital last week stoked longstanding Indian suspicions that Pakistan is unwilling, or unable, to stop militants on its soil from attacking India.

Rice cut short a European tour to go to India to meet Prime Minister Manmohan Singh who is under election-year pressure to craft a muscular response to opposition criticism that his ruling Congress party is weak on security.

In Washington, U.S. military officials said that Navy Admiral Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, had also travelled to the region on a similar mission.

"Adm. Mullen is in the area, as is Secretary Rice," U.S. Defense Secretary Robert Gates told reporters.