"We agreed that our meeting in New Delhi should be a historic opportunity for both our countries," he said. "This provides us the opportunity of meeting the hopes and aspirations of our peoples that we will succeed in turning a new page in our relations.

"We also agreed that the two foreign secretaries would be meeting soon to review and carry forward our bilateral agenda in the spirit of our meeting today."

Watch: New India PM Modi holds talks with Pakistani rival Sharif

India said earlier that Modi had conveyed during the meeting his concerns about militants using Pakistani soil to carry out acts of terrorism in India.

Sharif said accusations and counter-accusations did not help matters.

Modi "underlined our concerns related to terrorism", Indian Foreign Secretary Sujatha Singh said after the talks.

"We want peaceful and friendly relations with Pakistan. However, for such relations to proceed, it is important that terror and violence is brought to an end," Singh said. "There was discussion on trade and we noted that we were fully ready to fully normalise trade and economic relations."

The two leaders shook hands and smiled for the cameras earlier in the day on the steps of a government building in central New Delhi before a 50-minute meeting that ran over its allotted time.

Sharif arrived in New Delhi on Monday for Modi's swearing-in.

It was the first time an Indian prime minister had hosted a Pakistani leader for official talks in Delhi since the rupture in relations that followed the 2008 attacks in Mumbai, which killed 166 people.

The attacks were blamed on Lashkar-e-Taiba, a Pakistani militant group which is now accused of being behind an attack last week on an Indian diplomatic mission in western Afghanistan.

During yesterday's talks Modi also underlined his desire to improve commercial ties, Singh said.

"There was discussion on trade and we noted that we were fully ready to fully normalise trade and economic relations. Both prime ministers expressed their interest in having this done as early as possible," Singh said.

Annual trade between the two countries is presently worth around US$2.5 billion.

In his other meetings, Modi called on Sri Lankan President Mahinda Rajapaksa to speed up reconciliation with the island's ethnic Tamil minority after a decades-long separatist war that left at least 100,000 people dead.

"Sri Lanka should expedite the process of national reconciliation in a manner that meets the aspirations of the Tamil community for a life of equality and dignity in a united Sri Lanka," Singh said of the meeting. Millions of Tamils live in southern India.

Modi also thanked Afghan President Hamid Karzai for his country's help in repelling the attack on the Indian diplomatic mission.

The attack "only strengthened our resolve to work together for the development and reconstruction of Afghanistan, a sovereign Afghanistan, Afghan-led and Afghan-controlled", Singh said.

Beijing welcomes Narendra Modi government

China has welcomed the government of Prime Minister Narendra Modi, saying it wants to strengthen the sometimes troubled relationship.

Top Chinese diplomat Yang Jiechi met India's ambassador to Beijing yesterday to assure him of the "high importance" China attached to ties.

China was "ready to work with the new Indian government to maintain high-level contact, strengthen cooperation and communication in all areas, keep the good momentum in developing bilateral ties, and contribute to the peace and progress of Asia and the world", Yang told Ashok Kumar Kantha.

A day earlier, Premier Li Keqiang sent Modi a message of congratulations, saying maintaining strong relations was a top foreign policy priority.

India and China have grown closer in recent years, although their ties remain overshadowed by a territorial dispute and the legacy of a brief but bloody 1962 border war.

India's concerns about a rising China are sharpened by China's close ties with arch-rival Pakistan and its dominance in the global economy.