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.

“I come with, certainly, a belief that India can compete with anybody, anywhere,” Clinton said. “The more open India becomes over time, the greater the standards of living and opportunity for the broader number of people will be.”

India is exploring ways to make itself more open to Iran. A 56-member Iranian trade team arrived in New Delhi for talks with top Commerce Ministry officials Monday to discuss ways of strengthening business ties in sectors that do not fall under the international sanctions, such as pharmaceuticals and farm products.

“The future of India-Iran trade relations is very promising, even though there will be difficulties in the beginning. But in our talks today, I observed that the spirit among officials and traders here is positive,” said Yahya Ale-Eshagh, the president of Tehran Chamber of Commerce and Industry and Mines. After meeting with business leaders Tuesday, the team will head for India’s commercial capital, Mumbai, on Wednesday.

Trade delegates said they hoped to increase annual bilateral trade from $ 15 billion to $25 billion over the next four years.

The irony of their visit coinciding with Clinton’s discussions with India this week to cut back on its oil imports from Iran was not lost on those at the traders conference. Iran is India’s second-largest source of oil, after Saudi Arabia.

“Together, the potential of trade cooperation between the two countries can become an economic force to reckon with. That is why there are so many vested interests who do not want this to succeed,” Saif Mahmood, a member of the legal group formed to assist bilateral trade, said at the conference.

Clinton’s trip to India followed a harrowing week of diplomacy in Beijing negotiating the fate of activist Chen Guangcheng. She stopped in the capital of Bangladesh, Dhaka, over the weekend to meet with the country’s dueling female political leaders, Prime Minister Sheikh Hasina and the former head of the government, Khaleda Zia. Clinton also met with famed microcredit pioneer Muhammad Yunus.

On Sunday, she flew just over the border to Kolkata, a historic city that was once the capital of the British Indian empire.

Clinton’s motorcade raced from the airport to the city, passing a stretch of farmland dotted with office buildings under construction, signals of West Bengal’s ambition to become an investment hub for tech companies.

At the town hall meeting, held at a girls school, the moderator and members of the audience implored Clinton to run for U.S. president in 2016.

“I’m very flattered, but I feel like it’s time for me to step off the high wire,” she said. “I’ve been involved at the highest level of American politics for 20 years now. I’d like to come back to India and just wander around without having the streets be closed and a lot of security around.”

Clinton met for nearly an hour with one of the most famous women in India, Mamata Banerjee, chief minister of West Bengal state and a critical ally of the ruling Congress party. Banerjee, who is also known as “Didi,” meaning older sister, ended 34 years of Communist rule in West Bengal last year.

“I know for myself how difficult it is for women to get elected anywhere,” Clinton said in Kolkata. “When I meet a woman who’s broken through those barriers . . . we share a common bond, if you will, having gone through the fire of electoral politics.”