NEW DELHI--President Barack Obama and Indian Prime Minister Narendra Modi said they made tangible progress on a range of issues with movement on civil nuclear tradedefense cooperation and climate change.

With pageantry on full display, Mr. Obama was scheduled to appear at India's annual Republic Day parade on Monday, a first for a U.S. leader. But the results of talks on key trade and security issues were more nuanced.

Mr. Obama described a "breakthrough" in long-stalled talks on allowing U.S. firms to invest in nuclear power plants in India. But U.S. officials said work remains on implementation by India, and some U.S. corporate officials said they are evaluating the outcome of the talks in New Delhi.

Both leaders touted security agreements, including renewal of a defense pact and a deal to jointly produce new defense technology. And Mr. Obama said they agreed on steps to promote clean energy and to tackle climate change. "India's voice is very important on this issue," Mr. Obama said.

None of Sunday's discussions amounted to a major accord. Still, coming on the heels of Mr. Modi's trip to Washington in September, both leaders declared the visit an unqualified success.

"We have agreed that India and the United States must have regular summits at greater frequency," Mr. Modi said. "And we also established hot lines between myself and Barack and our national security advisers."

The burgeoning personal relationship between the two was on display from the moment of the arrival of the president and first lady Michelle Obama, when Mr. Modi departed from protocol and welcomed the U.S. president on the tarmac.

Mr. Obama greeted the Indian leader with an enthusiastic handshake and a hug.

The U.S. president later laid a wreath and planted a tree at a memorial to Mahatma Gandhi, a personal hero of Mr. Obama's.

The U.S. president attended a state dinner in his honor Sunday night.At a news conference, Mr. Obama joked that Mr. Modi had been received like a Bollywood star during his visit to the U.S. and said that the two leaders had compared sleep patterns.

"It turns out Mr. Modi is getting even less sleep than me," Mr. Obama said.

His itinerary originally included a visit Tuesday to the Taj Mahal. But just before Mr. Obama left Washington, the White House said the president would cut short his time in India and fly to Riyadh as Saudi Arabia mourns its late king. The scheduling change was viewed as a disappointment in India.

After extended talks Sunday, Messrs. Obama and Modi pointed to a pathway to resolving issues that have prevented U.S. firms from investing in nuclear power plants in India.

The two have been at an impasse over India's liability law, which would hold American suppliers responsible for accidents at the power plants they take part in building.

The U.S.-India nuclear deal, which was supposed to clear the way for the sale of nuclear reactors and fuel to India, was signed in 2008. But the 2010 passage of an Indian law making suppliers liable for accidents stalled progress.

Mr. Obama said he and Mr. Modi had achieved "breakthrough understandings" on two issues that were holding up progress, but he offered no specifics. Richard Verma, the U.S. ambassador to India, said teams from both countries had been working since September to resolve the liability issue and a second question of how to account for nuclear materials. After three meetings, the two sides reached an understanding that addressed both issues.

He said the governments were in agreement but that it would be incumbent upon U.S. companies to do their own risk assessment.

The agreement calls for a combination of insurance pools and Indian assurances that a "memorandum of law"--essentially an executive action--could be used to ensure that India is in compliance with international rules on liability.

"Now, ultimately, it's up to the companies to decide whether to go forward or not," he said. "But the two governments came a long way to reach an understanding."

A spokesman for GE-Hitachi Nuclear Energy, a prospective supplier, said the firm is reviewing the results of talks Sunday.

Ben Rhodes, a deputy White House national security adviser, called Sunday's agreement "a breakthrough," while noting that still left to do were the technical implementation of the deal and the companies" own determinations about whether to invest.

"But in our judgment, the Indians have moved sufficiently on these issues to give us an assurance that the issues are resolved and that there's a path open to implementation and investment here," he said.

Mr. Modi said a civil-nuclear agreement would be the centerpiece of a transformed U.S.-India relationship.

"Six years after we signed our bilateral agreement, we are moving toward commercial cooperation, consistent with our law, our international legal obligations, and technical and commercial viability," Mr. Modi said.

Mr. Obama has been pushing nations ahead of a summit in Paris later this year to reduce their carbon output, and has cited a landmark agreement with China's President Xi Jinping in November as a model.

In India, however, Mr. Obama said the U.S. would share more data and help India assess and adapt to climate change, and the two countries will pursue a global agreement at the Paris summit.

John Podesta, adviser to the president, said India's commitments on clean energy were more of an expansion of renewable energy use than an effort to shut down coal plants.

"They're going to continue to use a lot of coal in their system--they're trying to provide electricity to 400 million people," he said.

During Sunday's meeting, Mr. Modi told the U.S. president that climate change was "an article of faith for him," Mr. Podesta said.

William Mauldin contributed to this article.

Write to Colleen McCain Nelson at colleen.nelson@wsj.com

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