Speaking to reporters at the end of the first day of a four-day visit that will take him from Mumbai, the financial center of Asia's third-largest economy, to the capital New Delhi, Snow noted that India has been reluctant to lift the limits that it maintains on foreign participation.
India is only slowly phasing in more foreign participation in banking and private firms are allowed only up to 26 percent ownership in its insurance sector.
"It needs to allow foreign firms greater participation in insurance and banking and really across the board," the US Treasury chief said.
Earlier in the day, Snow met representatives of US firms doing business in India and he was having dinner with a group of Indian chief executives.
Snow's trip to India extends a series of visits to countries the US Treasury sees as having a vital role in shaping the global economy in the future. He visited Brazil in the summer and was in China last month.
He said that faster economic growth would help India deal with its problems of massive poverty and, at the same time, add stability by strengthening its capital markets.
"That's a large message, it's not really different from the message we were taking to China, that well-functioning financial markets are in a country's best interests," Snow said.
"To have well-functioning financial markets, you need deep and liquid markets with expertise and talent and you hurt yourself if you cap yourself off from resources and talent that's available around the world."
The Bush administration sees India, with its thriving service sector drawing US jobs away through outsourcing to an educated, cheaper labour force, as a regional leader with considerable influence in advancing the drive toward free trade.
"India is a stop along the way toward visiting all those countries - including China and Brazil which we visited earlier - that we regard as having the potential to become the major economies of the 21st century," Treasury Under Secretary for International Affairs Tim Adams said ahead of the visit.
Snow said India's commitment to building up its infrastructure - roads, railways, ports, airports and electricity-producing capacity - will be "a big part of where the country goes in the next three or four years" because it will help determine its ability to keep the economy expanding.
"These are all areas where America has expertise and there ought to be major opportunities for the US going forward as well as opportunities in the financial sector since America has a number of the world's first-tier financial firms." Snow said.
India's $700-billion economy has been growing at a rate of more than 6 percent on average over the past five years.
But the government estimates that about 260 million people - more than a quarter of the population - lives in poverty, without safe drinking water, proper sanitation facilities or two square meals a day.
Last week the Indian government approved setting up a state-run firm to fund such projects, something short of the private-enterprise solutions the Bush administration would favour.
When Snow moves on to New Delhi on Wednesday, he is to meet Finance Minister Palaniappan Chidambaram and Prime Minister Manmohan Singh.