U.S. President Barack Obama and new Indian Prime Minister Narendra Modi vowed on Monday to expand and deepen their countries' strategic partnership and make it a model for the rest of the world.

In a joint "vision statement" issued after their first meeting at a White House dinner, the two leaders said they would work together "not just for the benefit of both our nations, but for the benefit of the world."

They said their countries would cooperate in security and fight terrorism and back a "rules based" global order in which India assumes greater multilateral responsibility, including a reformed U.N. Security Council.

They also vowed to work together against the threat posed by climate change and to cooperate to address the consequences of unchecked pollution.

"We have a vision that the United States and India will have a transformative relationship as trusted partners in the 21st century. Our partnership will be a model for the rest of the world," the "vision statement" said.

The two leaders also said the two countries would work to ensure that economic growth brought better livelihoods for all people and stressed the importance of open markets and fair and transparent practices to allow trade to flourish.

The United States has been keen to expand business and security ties with India, which is sees as a key counterbalance to an increasingly assertive China in Asia. Obama has backed Delhi's bid to become a permanent member of the U.N. Security Council.

However, so far the relationship has failed to live up to his declaration in 2010 that it would become "one of the defining partnerships of the 21st Century."

Modi, who came to power in May, has received a warm welcome in the United States, even though he was denied a visa in 2005 over rioting in his home state three years earlier killed more than 1,000 people, mainly Muslims. Modi denies any wrongdoing and has been exonerated by an Indian Supreme Court probe.

Modi has maintained a frantic schedule during his visit, which began on Friday, even though he is fasting in accordance with Hindu custom and drank only warm water at the White House dinner.

As part of an effort to spur foreign investment, he met more than a dozen U.S. corporate leaders earlier on Monday and told them he was committed to liberalizing India's economy, which has underperformed other emerging markets recently after years of breakneck growth.

On Saturday, Modi addressed the U.N. General Assembly and then appeared before some 60,000 people at a musical event in New York's Central Park aimed at ending global poverty and bringing essentials such as sanitation to all.

On Sunday, he received a rapturous welcome from a big crowd of Indian-Americans in an appearance in New York's Madison Square Garden arena.

He will hold further talks with Obama and his administration on Tuesday.