(Updates with Modi arrives, talks begin)
WASHINGTON, June 26 (Reuters) - U.S. President Donald Trump and Indian Prime Minister Narendra Modi met for the first time on Monday, seeking to develop a warm relationship despite differences over trade, immigration and the Paris climate accord.
The two leaders went into their relatively low-key summit looking to bolster the U.S.-India strategic partnership but an equally important goal was simply to break the ice and get to know each other.
As they met, a Pentagon agency said the U.S. State Department has approved the possible sale to India of a Boeing C-17 transport aircraft with an estimated cost of $366 million.
Trump, in Oval Office remarks as Modi sat beside him, said Modi "has been such a great prime minister" and noted that he had been reading about India's economic success under his leadership.
"Economically, India is doing very well," he said.
Modi, on his fifth visit to the United States since becoming prime minister in May 2014, thanked Trump for a warm welcome.
Later, as he and Modi joined for talks with senior officials, Trump said the two leaders were making great progress.
"We agreed on most things and I would say by the end of the day well agree on everything," Trump said.
Trump administration officials have pointed to both leaders' impact on social media - each has more than 30 million Twitter followers - as proof that they are cut from the same cloth, and predicted the two would get along well.
The president's name is on a Trump Tower property in Mumbai and he spoke warmly of India during his presidential campaign last year.
"The White House is very interested in making this a special visit," said one senior official. "Were really seeking to roll out the red carpet."
Modi will try to strengthen ties that have appeared to loosen. Indian officials, noting both men's tendency to speak their mind, were anxious to see how they got along.
FIRST WHITE HOUSE DINNER
They will have one-on-one talks followed by statements to the news media without taking questions. They will then have a working dinner, the first time Trump has played host to a foreign dignitary at a White House dinner.
"If the chemistry is good, everything else gets sorted," said an Indian official. "The only way is up. How much up we go depends on the leaders. If they click, we go up higher."
Five U.S. senators signed a letter to Trump expressing concern about violations of religious liberty in India, including discrimination against religious-based aid groups, and asking him to make the issue a top priority during Modi's visit.
The letter was signed by Republicans John Kennedy, Roy Blunt, Mike Crapo and James Lankford, and Democrat Amy Klobuchar.
Sikh organizations planned a protest in front of the White House on Monday.
While progress is expected in defense trade and cooperation, there are frictions elsewhere between the United States and India.
Trump, who campaigned on an "America First" platform, has been troubled by the growing U.S. trade deficit with India. He has called for reform of the H-1B visa system, which has benefited Indian tech firms.
He set the United States on a path to withdraw from the Paris climate agreement and accused India of negotiating unscrupulously for the accord in order to walk away with billions of dollars in aid.
Meanwhile, Indian officials reject suggestions that Modi's "Make in India" platform is protectionist and complain about the U.S. regulatory process for generic pharmaceuticals and rules on fruit exports to the United States.
They stress the importance of the huge Indian market to U.S. companies and major growth in areas such as aviation, which offer significant opportunities for U.S. manufacturers. (Additional reporting by Patricia Zengerle; Editing by Steve Orlofsky and Bill Trott)