WASHINGTON, June 21 (Reuters) - U.S. President Joe Biden and Indian Prime Minister Narendra Modi are expected to deepen defense and technology cooperation between their countries during Modi's official visit to the White House, despite lingering concerns about human rights in India.

Two days of carefully orchestrated official events had a bumpy start on Wednesday afternoon, however, when Modi was so late to a planned tour of the National Science Foundation that the president's wife Jill Biden, a teacher, started without him.

Modi, who arrived about 30 minutes after the scheduled start of the tour, apologized. Later he came to the White House for a private dinner with the Bidens. The first couple and the prime minister smiled and laughed together outside the White House before going indoors. Modi will attend a state dinner on Thursday night, after addressing Congress and holding a rare press conference with Biden.

Washington wants India to be a strategic counterweight to China and sees India as a critical partner. Modi is seeking to raise the influence that India, the world's most populous country at 1.4 billion, has on the world stage.

Biden is expected to raise U.S. concerns about democratic backsliding in India under Modi's Hindu nationalist Bharatiya Janata Party during the visit, national security adviser Jake Sullivan told reporters on Tuesday. "We do so in a way where we don’t seek to lecture or assert that we don’t have challenges ourselves," he said.

U.S. companies are welcoming Modi warmly, and business agreements in artificial intelligence (AI), quantum computing and investments in India by Micron Technology (MU.O) and other U.S. companies are expected during the visit.

At his event with Jill Biden, Modi invited American students to come to India and said he was happy to meet "young and creative minds" as soon as he arrived in Washington. Modi said India was training students in AI and had started labs across the country.

More than 200,000 Indian students were studying in the United States as of last year, according to the White House.

Thursday's press conference is unusual. Modi has not addressed a single press conference in India since becoming prime minister about nine years ago. In May 2019, he attended a press conference in India but never took questions.