A joint statement called "on all countries to actively cooperate with the Indian authorities" to support efforts to find "the perpetrators, masterminds, sponsors...and everyone connected with these barbaric acts," the declaration adopted by the Indian prime minister and the Russian president said.
Terrorists swept through Mumbai on November 26, armed with submachine guns and grenades attacking hotels, the railway station, a cinema, and a hospital. The three-day rampage killed 174 people, including more than 20 foreigners.
Singh told journalists after the meeting, "We expect the international community to recognize that terrorism anywhere and everywhere constitutes a threat to world peace," and added without naming Pakistan that the "territory of the neighboring country had been used" to commit the terrorist acts.
The Indian government said the 10 terrorists, who travelled to Mumbai by sea from Karachi, had been trained in Pakistan. Investigators have said the only terrorist captured alive, 21-year-old Azam Amir Kasav, has confessed to receiving military training in Pakistan.
On Monday, India sent an official note to Pakistan's ambassador in New Delhi demanding the extradition of 20 people believed to be involved in terrorist activities, including three fugitives wanted in India.
Manmohan Singh and Dmitry Medvedev urged the international community to speed up the adoption of the Comprehensive Convention on International Terrorism, a draft of which is currently under discussion by the UN General Assembly.
India and Russia also called for the development of a single approach to countering terrorist threats which would also cover the security problems in Afghanistan.
Russia and India expressed concern about the deterioration in the security situation in Afghanistan which has resulted in intensified attacks by the Taliban across the country.