NEW DELHI —Secretary of State Hillary Rodham Clinton arrived in India’s capital Monday with a clear message for the country’s leaders: Cooperate with us on Iran.

Yet less than a mile from her meeting with Prime Minister Manmohan Singh, there was another group meeting with Indian leaders. An Iranian trade delegation is in New Delhi, overlapping with Clinton’s trip and potentially undermining one of its main purposes.

The Obama administration is turning up the pressure on India to join international sanctions against Iran that would choke off funds for the country’s nuclear program. India, which relies on Iran for about 12 percent of its oil imports, has so far been unwilling to go along.

“The United States and India share the same goal,” said Clinton at a joint press conference Tuesday morning with India's Minister of External Affairs S.M. Krishna. “We both want to prevent Iran from getting a nuclear weapon and India’s been a strong partner in urging Iran to live up to its international obligations.”

Time is running out for India to make a decision. Starting June 28, the United States will impose sanctions on any foreign bank or company engaging in oil transactions with the Iranian central bank. The European Union has agreed to a full embargo beginning July 1.

Clinton said the United States “commended” the steps taken so far by India to reduce its imports from Iran but urged its ally in the region to go further.

The United States needs as many partners as possible as it presses Iran to cooperate. Representatives from six countries, including the United States, met with Iran in April to negotiate, and more talks are expected with the United Nations later this month.

Clinton also had tough words for Pakistan during her trip, saying the country has fallen short in its pursuit of Hafiz Saeed, the suspected architect of the 2008 terrorist attacks in Mumbai, often called ‘India’s 9/11.’

“We’re well aware that there has not yet been the steps taken by the Pakistani government to do what both India and the United States have repeatedly requested them they do,” said Clinton at a town hall-style meeting in Kolkata Monday. “And we’re going to keep pushing that point.”

At the press conference Tuesday, she said, Pakistan “needs to make sure that its territory is not used as launching pads for terrorist attacks anywhere, including inside Pakistan. Because the great unfortunate fact is that terrorists in Pakistan have killed more than 30,000 Pakistanis.”

The Obama administration has tried to build a closer relationship with India. At the Kolkata event Monday, Clinton repeated Obama’s declaration that the United States’ relationship with India will be “one of the defining partnerships of the 21st century.”

Given shared concerns about security issues in China and Pakistan, some observers believe the world’s two biggest democracies would make natural partners. And trade between the countries has expanded steadily, from $9 billion in 1995 to $100 billion now.

But progress has been bumpy. Aside from the issue of sanctions against Iran, U.S. businesses have also been frustrated that India, unlike China, has not allowed retailers such as Wal-Mart to set up stores in the country and gain access to its booming middle class.