Trump and Modi pledged to work together to counter North Korea's "weapons of mass destruction" programs and vowed to hold "all parties" that support these programs accountable, the White House statement said.
Modi came to Washington looking to revitalise a relationship that thrived under former President Barack Obama but has appeared to flag as Trump courted India's rival China in an effort to persuade Beijing to do more to rein in North Korea.
Modi effusively praised Trump, hailing his "vast and successful experience in the business world" and "great leadership" for US-India ties, which he said should "lend an aggressive and forward looking agenda to our relations."
He said he had invited Trump to India but no time was given for a visit.
Modi harked back to Trump's "Make America Great Again" campaign slogan to stress that his agenda for his country was little different than Trump's.
"I am sure that the convergence of my vision for "New India" and President Trump's vision for making America great again will add new dimensions to our cooperation," he said.
Trump and Modi had a working dinner on Monday night, the first time Trump has played host to a foreign dignitary at a White House dinner.
Trump administration officials have pointed to both leaders' impact on social media - each has more than 30 million Twitter followers - as proof they are cut from the same cloth.
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