In an editorial, the New York Times said Clinton should assure New Delhi that Washington will keep pressing Pakistan to prosecute Mumbai attack suspects and shut down the LeT 'once and for all.'
"It is time for India to take more responsibility internationally and to do more to revive the world trade talks it helped torpedo last year and as a major contributor to global warming to join the developed countries in cutting greenhouse gas emissions," it said.
It said India "needs to do a lot more to constrain its arms race with Pakistan and global proliferation."
"Clinton should urge India to consider opening regional arms talks with Pakistan and China and drop its opposition to the test ban treaty," it said.
Noting that the prime focus of Prime Minister Manmohan Singh's government must be Pakistan, the paper said it is encouraged "that India and Pakistan have resumed their dialogue, interrupted after the 26/11 attacks."
"Clinton needs to assure India that Washington will keep pressing Pakistan to prosecute suspects linked to the Mumbai attacks and to shut down the Lashkar-e-Tayiba group of extremists once and for all," the editorial said.
The Secretary of State will hold talks with Prime Minister Manmohan Singh and External Affairs Minister S M Krishna in New Delhi on Monday.
"During the negotiations on the Indo-US nuclear deal, the Bush administration managed to persuade New Delhi to grudgingly support United Nations Security Council sanctions against Iran's nuclear programs. India now needs to do more," the article said.
The New York Times said India also needs to help allay Pakistan's fears.
"If resolving tensions over Kashmir their biggest flashpoint is not possible while Pakistan is battling the Taliban, then talks on water and environmental issues may be an interim way to seek common ground," it said.
The paper said one of the many concerns about the nuclear deal was that it would make it easier for India to expand its arsenal and drive Pakistan to produce more of its own weapons.