US President Barack Obama is holding talks with Indian PM Manmohan Singh on the third day of his visit to India.
Ahead of the meeting he said ties between the countries was one of the "defining partnerships" of the 21st Century.
Mr Obama arrived in the capital Delhi on Sunday afternoon, from Mumbai where he announced $10bn (£6.2bn) in new trade deals with India.
The US president is on a 10-day Asian tour designed to boost US exports.
After a ceremonial welcome at the Indian president's palace on Monday, Mr Obama said India was "already a world power". He also laid a wreath at a memorial to Indian independence leader Mahatma Gandhi.
"The partnership between the United States and India will be one of the defining partnerships of the 21st century," Mr Obama said ahead of his meeting with Mr Singh.
He said the aim of his talks with the prime minister, president and other Indian leaders would be to strengthen co-operation between and discuss issues like "counter-terrorism and people to people contact".
Mr Obama is expected to elaborate on his vision for US relations with India in his address to the Indian parliament.
Mr Obama is also expected to meet Congress party president Sonia Gandhi and opposition leader Sushma Swaraj.
Speaking with a group of students in Mumbai on Sunday, Mr Obama called for dialogue between India and Pakistan, adding that India was the country with the biggest stake in Pakistan's success.
US support for Pakistan is one of the most sensitive issues Mr Obama faces during his visit, says the BBC's Mark Dummett in Delhi.
Many Indians think the US cannot be trusted as long as it continues to supply weapons to Pakistan's army, this country's "enemy number one", our correspondent adds.
In Mumbai, Mr Obama visited the scene of the 2008 attacks, saying India and the US were united against terrorism.
He also criticised the pace of Pakistan's fight against militants within its borders.
Trade between India and the US was worth about $40bn in 2008 - still significantly less than US trade with other partners like China and Europe.
Later on his trip, Mr Obama will announce a "comprehensive partnership" including economic ties in Indonesia, attend a G20 summit of global economic powers in Seoul and participate in an Asia-Pacific economic forum in Yokohama, Japan.