Bebeto Matthews, Associated Press
India's Prime Minister Narendra Modi speaks during a press conference at the Council on Foreign Relations, Monday, Sept. 29, 2014 in New York. President Barack Obama and Modi said Tuesday that "it is time to set a new agenda" between their countries, addressing concerns that the world's two largest democracies have grown apart.

WASHINGTON — President Barack Obama and India's new Prime Minister Narendra Modi said Tuesday that "it is time to set a new agenda" between their countries, addressing concerns that the world's two largest democracies have grown apart.

The leaders planned an Oval Office meeting Tuesday as the centerpiece of Modi's two-day visit to the White House and described their agenda in an op-ed that appeared on The Washington Post website. They said they will explore ways to expand collaboration on trade, investment and technology "that harmonize with India's ambitious development agenda, while sustaining the United States as the global engine of growth."

"The true potential of our relationship has yet to be fully realized," the leaders wrote. "The advent of a new government in India is a natural opportunity to broaden and deepen our relationship. With a reinvigorated level of ambition and greater confidence, we can go beyond modest and conventional goals. It is time to set a new agenda, one that realizes concrete benefits for our citizens."

Obama hosted Modi for a private dinner Monday — despite the fact that Indian leader, a devout Hindu, was fasting.

Typically, visiting heads of state spend just a portion of a day at the White House meeting with Obama and other U.S. leaders. The rare second day of attention from Obama underscored the White House's desire to give a warm welcome to a man who was once barred from even entering the U.S. Monday evening,

Now the leader of the world's largest democracy, Modi was the top elected official in the Indian state of Gujarat more than a decade ago when religious riots there killed more than 1,000 Muslims. When Modi later requested a visa to visit the U.S., Washington said no. Modi has denied involvement in the violence.

Obama and Modi wrote they also plan to discuss shared intelligence on terrorism and regional concerns, including Afghanistan, where the U.S. is winding down its 13-year military involvement. They also said the agenda includes clean energy, climate change, medical collaboration to fight diseases and scientific efforts to improve sanitation and hygiene throughout India.

While military ties and defense trade between the two countries have grown, the economic relationship has been rockier, with Washington frustrated by India's failure to open its economy to more foreign investment and address intellectual property complaints. Challenges with an existing civil nuclear agreement and the arrest and strip search last year of an Indian diplomat have further fraying relations.

Ahead of Modi's visit to Washington, he was given a rock star reception at New York's Madison Square Garden, where thousands of Indian-Americans flocked for a rare chance to see the new leader. The dazzling Bollywood-style dancers and dozens of U.S. lawmakers who took part highlighted the popular support Modi is enjoying on his first official visit to the U.S. since being elected in May.

Associated Press writer Darlene Superville contributed to this report.