NEW DELHI (Reuters) - The United States and India could soon reschedule a visit by the U.S. Energy Secretary that was cancelled because of a diplomatic row, New Delhi said in a statement after foreign minister Salman Khurshid met his counterpart John Kerry.

"Both sides looked forward to the early realization of the mutually-agreed calendar of bilateral exchanges," India's foreign ministry said in a statement after the two men met in Montreux on the sidelines of a conference about Syria.

The statement mentioned a visit by Ernest Moniz, the U.S. energy secretary, who postponed the trip earlier this month because of a dispute over the arrest and strip search of an Indian diplomat in New York on charges of visa fraud and lying about how much she paid her housekeeper.

The meeting, on Wednesday, was the highest level exchange since the spat. In December, Kerry expressed regret for the incident in a phone call to India's National Security Adviser. He also tried to call Khurshid, but could not reach him.

No firm timeline was given for the trip to India by Moniz, or other outstanding visits.

The argument plunged ties between the friendly nations to the lowest point in 16 years before a deal was struck and the diplomat, Devyani Khobragade, returned to India.

Relations have still not returned to normal, and Khurshid made a point of questioning Kerry about the use of visas reserved for human trafficking cases to evacuate the housekeeper's husband and children from India.

The statement also said "outstanding issues" related to privileges and immunities of diplomats in both countries were discussed.

India sharply curtailed privileges granted to U.S. diplomats stationed in the country after the arrest, to bring the them on a par with the treatment of Indian diplomats in the United States.

(Reporting by Frank Jack Daniel)