At the start of a three-day U.S. presidential visit rich with pageantry and symbolism, President Obama and Indian Prime Minister Narendra Modi said Sunday that the two countries have made progress toward resolving a long-standing impasse on civilian nuclear cooperation.

Obama said that the United States and India have reached a “breakthrough understanding” that would make it easier for U.S. firms and others abroad to invest in Indian nuclear power plants. Indian law holds suppliers, designers and builders of plants liable in case of an accident, making companies reluctant to invest in the plants. The two countries have also long failed to agree on how to track nuclear material.

The new understanding, although short on specifics, addresses two of a number of nuclear-related issues that have hamstrung relations for years, preventing implementation of a landmark civilian nuclear deal reached during the George W. Bush administration.

“We’re committed to moving towards full implementation,” Obama said. “And this is an important step that shows how we can work together to elevate our relationship.”

The White House said the agreement involved the provision of insurance pools and an assurance that reducing liability would be within the framework of the 2008 agreement. It will now be up to companies to decide whether to do business in India.

President Obama arrived in New Delhi, India, ahead of the country’s Republic Day celebrations. (Reuters)

U.S. Ambassador Richard Verma said that the understanding was reached under the Indian system “through a memorandum of law” and would not require additional legislation.

Some voiced skepticism following Sunday’s brief announcement.

“The Indian government is going to town saying ‘breakthrough, breakthrough,’ but there are a lot of questions that still remain,” said R.R. Subramanian, a senior scholar of nuclear disarmament at the Institute for Defense Studies and Analyses in New Delhi.

U.S. companies and their advisers, meanwhile, said they had received no details about an agreement on liability or the tracking of U.S. nuclear materials that would be exported to India. On the liability issue, Bloomberg News quoted an Indian official as saying that an insurance pool worth $122 million would be set up, with the government contributing an unspecified amount at a later date.

A key adviser to U.S. nuclear contracting firms — who spoke on the condition of anonymity to protect business relationships — said, “That doesn’t do it.”

Christopher White, a spokesman for nuclear construction firm GE Hitachi Nuclear Energy, said in a statement that the company “applauds the efforts of the U.S. and Indian governments” and that “we look forward to reviewing the governmental agreement.” White said GE Hitachi wants an agreement that “brings India into compliance with the International Convention on Supplementary Compensation,” which would cap liability in case of a disaster.

U.S. nonproliferation experts also questioned whether Obama has the authority to waive a requirement to track nuclear materials that is part of the 2006 legislation that eased other restrictions on exporting to India. “It would appear that the U.S. side has caved on a requirement set by Congress in the ‘Hyde Act’ of 2008 for implementation of any nuclear cooperation between the two countries that there must be an extensive ‘end-use monitoring’ program to help ensure that no U.S.-origin nuclear material or technology is diverted for military purposes,” Daryl G. Kimball, executive director of a nongovernmental group called Arms Control Association, wrote in an e-mail to National Security Council officials asking for clarification.

Bernadette Meehan, an NSC spokesman, responded: “The United States is satisfied that the information we will receive . . . including through information exchanges and a consultative mechanism, will provide enough information to meet the requirements under the 123 agreement [of the U.S. Atomic Energy Act], as well as allow for the necessary certifications to Congress as required by the Hyde Act.”

But, Kimball said in an e-mail to The Washington Post, “India, which has nuclear weapons and is building up its nuclear weapons program outside of international safeguards/monitoring, is a special case. It means that additional safeguards are necessary to ensure that U.S. nuclear cooperation does not directly or indirectly assist its nuclear weapons program.”

Former prime minister Manmohan Singh staked his first term on the nuclear agreement, which ended India’s three decades of nuclear isolation and held out the promise of billions of dollars in sales and thousands of jobs for U.S. energy companies. The U.S. government and private sector were stunned when India’s Parliament passed the liability law in 2010.

In the years since, India’s enthusiasm for nuclear power has been dampened by the nuclear disaster in Japan in 2011 and the difficulty of securing land on which to build nuclear reactors. Nuclear power today represents only about 2 percent of India’s total installed power capacity.

Obama and Modi said they had also made progress on other issues, including climate change, saying they are committed to phasing out carbon emissions and pursuing a “strong global climate agreement” at talks in Paris later this year. The two countries reached an agreement in September to help India shift to renewable fuels.

Asked whether the United States’ climate deal with China had put pressure on India to cut its emissions, Modi said that “India is an independent country.” He added that “there is no pressure on us from any country or any person” but that there is pressure on all people to combat climate change.

Renewable energy is scarce and expensive here, and about 300 million people live without power. Coal power is growing rapidly.

The two countries also renewed their 10-year defense framework agreement and agreed in principle to pursue co-development of weapons. “Our relationship stands at a new level today,” Modi said.

The apparent progress was, in many ways, dwarfed by talk of the budding close relationship between the two men, which started when Modi came to Washington in September as the two countries looked to revive their stagnating relationship.

Modi broke with tradition and met Obama at the airport here, giving the president a bear hug after he bounded down from Air Force One. Obama was welcomed at a ceremony at the presidential palace on a cool, foggy afternoon, traveling there in a limousine trailed by dozens of red-clad men on horseback and receiving a 21-gun salute. On Sunday night, he and first lady Michelle Obama attended a state dinner at the palace.

“Barack and I have forged a friendship,” Modi said earlier through an interpreter. He made a statement in English and answered questions in Hindi. “There is openness when we talk, and we even joke and share a lot together,” he said. “I think this is a chemistry which has not only brought Washington and Delhi, Barack and I, closer, but also the two peoples of the two countries closer.”

Obama is the first president to visit India twice while in office, after receiving an unprecedented invitation to attend the country’s annual Republic Day parade, which celebrates the adoption of the Indian constitution.

The personal relationship between him and Modi blossomed during the Indian premier’s Washington visit in September. The two men talked over a lavish dinner, even though Modi was on a religious fast, and visited the Martin Luther King Jr. memorial, where they invoked Mohandas K. Gandhi. On Sunday, Obama visited the site that holds Gandhi’s ashes, walking slowly around the memorial and scattering rose petals on it.

His friendship with Modi was somewhat unexpected. Obama tends to be reticent among world leaders, rarely striking up friendships in the way that his predecessor, George W. Bush, did. The notable exception is British Prime Minister David Cameron, whom Obama has on occasion called “bro.”

The rapport between the two men, forged over talk of campaigning, governing and ascending politically from humble backgrounds, came shortly after Modi was elected — and the two countries saw his U.S. trip as a way to try to revive their relationship. At the time, India felt overlooked by the administration’s focus on other Asian countries, and the United States was beginning to realize that it needs India as a counterweight to China.

“I think, from the very beginning, there were quite a few things that actually led to that personal affinity and that ability to build rapport,” said Phil Reiner, senior director at the National Security Council for South Asia.

In many ways, it remains surprising that Modi has become the leader to advance the U.S.-India relationship. In 2005, the State Department revoked his visa on the grounds that he had violated religious freedom by not doing enough to stop Hindu-Muslim riots in 2002 while he was chief minister of the state of Gujarat. More than 1,000 people were killed.

Steven Mufson in Washington and Annie Gowen and Rama Lakshmi in New Delhi contributed to this report.