Prime Minister Atal Bihari Vajpayee told reporters the explosions in the desert, 330 miles southwest of New Delhi, did not release radiation into the atmosphere.
The news stunned the world Monday, triggering fears of increasing nuclear tensions with neighbors Pakistan and China. India and Pakistan have fought three wars in the last 50 years.
"These were contained explosions like the experiment conducted in May 1974," Vajpayee said in a brief statement. He refused to take questions.
He said the devices tested were a fission device, a low-yield device and a thermonuclear device. "I warmly congratulate the scientists and engineers who have carried out these successful tests," Vajpayee added.
In Washington, White House press secertary Mike McCurry said the U.S. "is deeply disappointed by the decision of the government of India to conduct three nuclear tests. This runs counter to the effort the international community is making to promulgate a comprehensive ban on such testing."
President Clinton is scheduled to visit India and Pakistan this year, but McCurry said, "It's impossible to tell what the impact is on the trip at this point."
India, Pakistan and Israel are the three nations widely suspected of nuclear capability that have not joined the 1970 nuclear non-proliferation treaty, which is now observed by 185 countries.
In Vienna, a spokesman for the International Atomic Energy Agency, David Kyd, said India gave no advance warnings of the nuclear tests. Since India is a not a member of the treaty, it is not obliged to submit their nuclear facilities to IAEA inspection.
Since conducting a peaceful nuclear explosion in 1974, India "has not been prepared to state publicly whether they have a weapons capability or not," Kyd added.
Canadian Foreign Minister Lloyd Axworthy said the Group of Eight major industrial nations, the United States, Britain, Germany, France, Canada, Italy, Japan and Russia, would have to spell out its concerns at the May 15-17 meeting in Birmingham, England.
Vajpayee's government, which came to power in March, says India needs nuclear weapons to prevent what it calls military adventurism by neighboring Pakistan.
India first demonstrated its nuclear capability with the 1974 test explosion.