NEW DELHI — India tested a long-range ballistic missile capable of carrying nuclear weapons on Thursday, paving the way for membership to a small list of countries with access to intercontinental missiles and putting most of China in its reach.

The ballistic missile, called Agni 5, was launched from Abdul Kalam Island, off Odisha State in eastern India on Thursday morning, traveling for around 19 minutes and 3,000 miles. In a statement, the Indian Ministry of Defense said that all objectives of the mission had been “successfully met.”

The firing of the Agni-5 comes months after the official end of a standoff between China and India over a remote sliver of land in the Himalayas, a squabble that lasted for more than two months and that was one of the worst border disputes between the countries in 30 years. The launch also comes during a tense period in India’s troubled relationship with Pakistan, its nuclear-armed neighbor.

Nitin A. Gokhale, an independent national security analyst in New Delhi, said India did not previously have a missile capable of hitting “high-value targets” in China. But Thursday’s successful launch of the Agni 5 has changed the calculus, he said, putting most of China, including major eastern coastal cities such as Shanghai, in reach.