Putin and Vajpayee have already met several times recently
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The leaders of India and Russia have reaffirmed the strength of their countries' strategic partnership.
Indian Prime Minister Atal Behari Vajpayee met Russian President Vladimir Putin in the Kremlin on Wednesday during a three-day visit to Moscow.
The two men also proposed a number of "crucial steps" to counter the threat of international terrorism.
Russia is India's largest supplier of military hardware, and defence and economic ties were high up the agenda.
In a joint statement, the two leaders said that Russia and India favoured setting up of a "comprehensive system of collective security based on the supremacy of law".
`Threat of Taleban's return'
They also called for the "rapid restoration of the sovereignty of Iraq" under the United Nations.
The Indian prime minister expressed concern over the re-emergence of the Taleban in Afghanistan.
"Events are causing anxiety. There exists a threat of the Taleban's return in one form or another," Mr Vajpayee was quoted by the AFP news agency.
Both India and Russia have a stake in Central Asia and Afghanistan, and face threats from Islamic militancy.
Mr Vajpayee, who has been given the full red-carpet treatment including a private dinner at President Putin's out-of-town-residence, will also talk business during his visit.
He is accompanied by nearly 100 businessmen as Moscow and Delhi want to boost mutual trade which is stagnating at $1.4bn.
The Indian prime minister's second trip to Russia this year underlines how much the two countries are committed, first and foremost, to boosting trade, according to the BBC's Steven Eke.
Defence cooperation is the big success in the relationship of the Cold War allies.
The first joint naval exercises since the break-up of the Soviet Union were held this summer.
Designers from both the countries are working on a joint fighter jet.
Mr Vajpayee arrived in Moscow on Tuesday.
From Moscow, Mr Vajpayee will be going to Tajikistan and Syria before returning home next week.