NEW DELHI (AP) ― President Barack Obama and Indian Prime Minister Narendra Modi on Sunday declared an era of “new trust’’ in the often fraught relationship between their nations as the U.S. leader opened a three-day visit to New Delhi.

Standing side by side at the stately Hyderabad House, Obama and Modi cited progress toward putting in place a landmark civil nuclear agreement, as well as advances on climate change and defense ties.

But from the start, the day was more about putting their personal bond on display. Modi broke with protocol and wrapped Obama in an enthusiastic hug after Obama got off Air Force One.

Obama later told reporters that Modi’s “strong personal commitment to the U.S.-India relationship gives us an opportunity to further energize these efforts.’’

Modi was as effusive. He called Obama by his first name and said “the chemistry that has brought Barack and me closer has also brought Washington and Delhi closer.’’

The centerpiece of Obama’s visit was Monday’s annual Republic Day festivities, which mark the anniversary of India’s democratic constitution coming into force. Obama was attending as the parade’s chief guest, the first American president to have that honor.

The celebrations got underway on a foggy, rain-soaked morning in New Delhi with the parade that is part Soviet-style display of India’s military hardware, part Macy’s Thanksgiving Day-type parade with floats highlighting India’s cultural diversity. The route goes past the imposing India Gate monument and a memorial to the unknown soldier.

Obama’s presence would have been unlikely only a few years ago.

Relations between the U.S. and India hit a low in 2013 after an Indian diplomat was arrested and strip-searched in New York over allegations that she lied on visa forms to bring her maid to the U.S. while paying the woman a pittance. The official’s treatment caused outrage in New Delhi, and India retaliated against U.S. diplomats.

The U.S. and India also were at an impasse over implementing the civil nuclear agreement signed in 2008. The U.S. insisted on tracking fissile material it supplied to India. Also, Washington was frustrated by Indian legal liability provisions that have discouraged U.S. companies from capitalizing on new energy development in India because of concerns about their legal responsibilities in the event of a nuclear power plant accident

On Sunday, Obama said he and Modi had reached a “breakthrough understanding’’ on those areas of disagreements. Details on an accord were sparse.

Ben Rhodes, Obama’s deputy national security adviser, said only that India “moved sufficiently on these issues to give us assurances that the issues are resolved.’’ U.S. Ambassador Richard Verma said the agreement would not require new legislation.

The U.S. and India also agreed to extend a 10-year defense partnership deal and cooperate on the phasedown of hydroflurocarbons, the greenhouse gases used for refrigeration and air conditioning.

Still, that was hardly the kind of sweeping climate change agreement the U.S. ultimately has in mind with India. The White House is hoping that the surprise deal with China late last year setting ambitious targets for cutting greenhouse gas emissions will influence India and others.

Modi, however, rejected comparisons with China. “India is an independent country, and there is no pressure on us from any country or any person,’’ he told reporters Sunday.

Obama arrived Sunday morning to a capital whose normally bustling streets were empty. Police cleared sidewalks as Obama’s motorcade sped to the presidential palace for a welcome ceremony. Obama then visited a memorial to the father of India’s independence movement, Mohandas K. Gandhi.

Obama and Modi spent much of the afternoon in private talks. They broke briefly for a stroll through the gardens of Hyderabad House, the guest house where the leaders held their discussions. Sitting down before cups of tea, both men looked relaxed. They smiled and laughed often as they chatted animatedly.