He was speaking in Mumbai at the start of a 10-day Asian tour designed to boost US exports and create jobs.

Obama also announced an easing of US export controls and rejected caricatures of India as a nation of "call centres."

Visiting the scene of the 2008 attacks in Mumbai, he said India and the US were united against terrorism.

"We will never forget," he said at a memorial to victims of the attack by Islamic militants.

The outdoor memorial is a fountain with floating flowers just off the lobby of the Taj Mahal Palace hotel, where he and his wife are staying as guests.

He described the hotel as a symbol of India's "strength and resilience". He also wrote in a memorial book: "The United States stands in solidarity with all of Mumbai and all of India in working to eradicate the scourge of terrorism."

More than 170 people died in a series of co-ordinated attacks across the city in November 2008.