Footage showed the rocket with a range of more than 5,000 km (3,100 miles) blasting through clouds from an island off India's east coast. It was not immediately clear how far the rocket flew before reaching its target in the Indian Ocean.
The defense minister said the test was "immaculate".
"Today's successful Agni-V test launch is another milestone in our quest to add to the credibility of our security and preparedness," Prime Minister Manmohan Singh said in a message to the scientists who developed the rocket.
Almost entirely Indian-made, the Agni-V is the crowning achievement of a program developed primarily with a threat from neighboring China in mind. It will not be operational for at least two years, the government says.
Only the U.N. Security Council permanent members - China, France, Russia the United States and Britain - along with Israel, are believed to have such long-range weapons.
Fast emerging as a world economic power, India is keen to play a larger role on the global stage and has long angled for a permanent seat on the Security Council. In recent years it has emerged as the world's top arms importer as it upgrades equipment for a large but outdated military.
"It is one of the ways of signaling India's arrival on the global stage, that India deserves to be sitting at the high table," said Harsh Pant, a defense expert at King's College, London, describing the launch as a "confidence boost".
The launch, which was flagged well in advance, has attracted none of the criticism from the West faced by hermit state North Korea for a failed bid to send up a similar rocket last week.
China's Foreign Ministry said the two countries should "work hard to uphold friendly strategic cooperation", and for peace and stability in the region.
"China and India are large developing nations. We are not competitors but partners," the Chinese ministry spokesman, Liu Weimin, said when asked about the missile test at a briefing.
The Global Times tabloid, which is owned by the Chinese Communist Party's main mouthpiece the People's Daily, struck a less conciliatory tone.
"India should not overestimate its strength, "the paper said in an editorial published before the launch, which was delayed by a day because of bad weather.
India has not signed the non-proliferation treaty for nuclear nations, but enjoys a de facto legitimacy for its arsenal, boosted by a landmark 2008 deal with the United States.
On Wednesday, NATO said it did not consider India a threat. The U.S. State Department said India's non-proliferation record was "solid", while urging restraint.
"NO ARMS RACE - MUTUALITY"
India says its nuclear weapons program is for deterrence only. It is close to completing a nuclear submarine that will increase its ability to launch a counter strike if it were attacked.
India lost a brief Himalayan border war with its larger neighbor, China, in 1962 and has ever since strived to improve its defenses. In recent years the government has fretted over China's enhanced military presence near the border.
It is buying more than 100 advanced fighter jets, likely Rafales built by France's Dassault, in one of the largest global arms deals.
Even so, slow procurement procedures and corruption scandals mean its army, the world's second biggest, relies on critically outdated guns and suffers ammunition shortages.
Defense analyst Uday Bhaskar said India was not in an arms race with China, which has far greater capabilities, including missiles with a range closer to 10,000 km (6,000 miles).
"As and when Agni-V moves from technological proficiency to assured, credible and proven operational induction - maybe by 2014 - India will move towards acquiring that elusive mutuality it seeks with China," Bhaskar said in a column for Reuters.
Thursday's launch may prompt a renewed push from within India's defense establishment for a fully fledged intercontinental ballistic missile (ICBM) program, with weapons capable of reaching the Americas, though some of India's allies may bridle at such an ambition.
"Policy-wise it becomes more complicated from now on, until Agni-V, India really has been able to make a case about its strategic objectives, but as it moves into the ICBM frontier there'll be more questions asked," said Pant.
The Agni-V is the most advanced version of the indigenously built Agni, or Fire, series, part of a program that started in the 1960s. Earlier versions could reach old rival Pakistan and Western China.
The three stage rocket is powered by easier-to-use solid rocket propellants, can carry a 1-tonne nuclear warhead and is road mobile.
Source : Afghan Voice Agency (AVA), International Service