Analysts say the meeting will help to ease tensions
The leaders of India and Pakistan have met for the first time since last November's Mumbai (Bombay) attacks.
Indian PM Manmohan Singh and Pakistani President Asif Ali Zardari held talks on the sidelines of a summit in the Russian city of Yekaterinburg.
Mr Singh said he had to tell Mr Zardari that Pakistani territory must not be used for terrorism against India.
Relations between the two countries nosedived after Delhi said the Mumbai gunmen were from Pakistan.
More than 170 people died in the attacks, including nine gunmen.
Pakistan denied any responsibility in their immediate aftermath, but later admitted they had been partly planned from its soil.
The sole surviving suspected gunman is Pakistani and is currently on trial in Mumbai.
"I am happy to meet you, but my mandate is to tell you that the territory of Pakistan must not be used for terrorism," Mr Singh told Mr Zardari at the meeting.
Pakistan's foreign minister described the meeting as a "positive development" and played down any suggestion that Mr Singh's frank words had got proceedings off to a difficult start.
The BBC's Jill McGivering says the meeting was never expected to produce a breakthrough formula for reviving the stalled peace process.
But, she adds, the fact that the two leaders met at all is a positive sign and a measure of growing political willingness to seek new momentum.
Pakistani officials said after the meeting that foreign ministry officials from both countries will meet soon to discuss pertinent issues.
More than 170 people died in the attacks in Mumbai last November
Mr Singh had said earlier this month that his government would seek to mend fences with Pakistan provided it cracked down on militants, in an address India's newly-constituted parliament. The statement did not represent any dramatic shift in policy.
Our correspondent says that for both leaders, any attempt to compromise is hampered by strong public suspicion at home. While Mr Singh has been under considerable pressure to act tough, Pakistan is being urged by the US to improve its relationship with India so it can concentrate on tackling the insurgency on its own soil.
Pakistan's military is engaged in a series of offensives against Taliban militants across the north-west of the country.
India and Pakistan both have observer status in the Yekaterinburg summit for the Shanghai Cooperation Organisation, which include Russia, China and former Soviet Central Asian republics.
India pulled out of long-running peace talks with Pakistan following the Mumbai attacks.
It has since accused Pakistan of "not being serious enough" about bringing those who planned the Mumbai attacks to justice.
The recent release on bail of Hafiz Saeed, the head of the Islamic charity Jamaat-ud-Dawa, put further strain on relations between the two countries.
The charity is accused of being a front for Lashkar-e-Taiba, the group India says carried out the attacks.
Jamaat-ud-Dawa - listed by the US as a terrorist organisation - denies any links with militants.