NEW DELHI, Jan 23 (Reuters) - The new U.S. Secretary of State Hillary Clinton and India's foreign minister Pranab Mukherjee agreed on Friday to build on an "excellent bilateral relationship" between the two countries, a statement said.

Clinton telephoned Mukherjee amid heightened tensions between India and its nuclear-armed rival Pakistan, and a day after the new Obama administration appointed Richard Holbrooke as a U.S. special envoy to Afghanistan and Pakistan.

India is trying to mount a diplomatic offensive against its neighbour after attacks in Mumbai in November that India blames on Pakistan-based militants backed by some state agencies.

Islamabad strongly denies involvement and condemned the attacks, which killed 179 people.

"Both Ministers agreed that they would like to further strengthen the excellent bilateral relationship between India and the USA," an Indian government statement said.

Mukherjee could take over prime ministerial responsibilities from Manmohan Singh, as Singh will undergo coronary artery bypass surgery on Saturday and will take time to recovery.

New Delhi and Washington signed a civilian nuclear deal in 2008 under U.S. President Barack Obama's predecessor George W. Bush, reversing decades of U.S. non-proliferation policies, and bilateral ties are at their closest for years. (Reporting by Matthias Williams; Editing by Charles Dick)

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