Patrushev is expected to meet External Affairs Minister S Jaishankar and the Prime Minister.
National Security Advisor Ajit Doval meeting his Russian counterpart Nikolai Patrushev in Delhi for high level inter-governmental consultations on Afghanistan. The meeting was an outcome of a recent telephone conversation between PM Modi and Russian President Vladimir Putin.
The Doval-Patrushev talks delved into security implications of the Taliban's capture of power for India, Russia and the Central Asian region as a number of dreaded terror groups including Jaish-e-Muhammad and Lashkar-e-Taiba having a strong presence in the war-torn country, people familiar with the meeting said.
A Russian read-out of the delegation-level talks said attention was paid to intensifying joint work by "special services and military bodies" of both the countries and that emphasis was given on further interaction on the "anti-terrorist track", combating illegal migration and drug trafficking.
It is learnt that Chief of the Central Intelligence Agency (CIA) Burns, accompanied by a few officials, paid a quiet visit to India primarily to discuss ways to mitigate security threats that may emanate from Afghanistan.
The CIA chief held talks with Doval and a number of senior officials of the National Security Secretariat on Tuesday.
When asked about the visit, the US embassy declined to comment. There was no comment from the Indian security establishment as well.
It is learnt that Moore also held extensive talks with Doval during his brief visit.
Asked about the MI6 chief's trip to India, a British High Commission spokesperson said: "We do not comment on intelligence matters."
India has been in touch with all leading powers on the developments in Afghanistan following the withdrawal of troops by the US.
Three weeks after taking control, the Taliban on Tuesday a unveiled a "caretaker" government, saying it would be headed by Mohammad Hasan Akhund.
"As a follow-up to the telephone conversation between Russian President Vladimir Putin and Indian Prime Minister Narendra Modi on August 24, an exchange of views took place on the military, political and socio-economic situation in Afghanistan," the Russian read-out said.
It said the two sides agreed to coordinate on the Afghan issue in multilateral formats.
"They also touched upon humanitarian and migration problems in this country, as well as prospects for the Russian-Indian joint efforts aimed at creating conditions for launching a peaceful settlement process on the basis of an intra-Afghan dialogue," it said.
"The importance of defining parameters of the future state structure of Afghanistan by the Afghans themselves, as well as the need to prevent the escalation of violence, social, ethnic and confessional contradictions in the country, were emphasised," it added.
The people cited above said both India and Russia share similar concerns on terrorism that could flow out of Afghanistan.
The two sides also deliberated on threats from drugs networks operating from Afghan territory, the role of regional countries and details of Indo-Russia cooperation to meet the current and future challenges, they said.
The people said the consultations reflect the close, trusted, special and privileged strategic partnership between India and Russia that has significantly matured over time.
They said both sides exchanged each other's assessment on possible security implications of the Taliban's capture of power in Kabul and how a coordinated approach can be followed to confront any possible challenge.
Modi and Putin had on August 24 discussed the developments in Afghanistan and expressed the view that it was important for the two countries to work together.
On Tuesday, the Ministry of External Affairs said Patrushev is visiting India at the invitation of Doval for the high-level India-Russia inter-governmental consultations on Afghanistan.
After the Modi-Putin conversation, Russia said the two leaders expressed the intention to enhance cooperation to counter the dissemination of "terrorist ideology" and the drug threat emanating from Afghanistan and agreed to form a permanent bilateral channel for consultations on the issue.
On Monday, Russian envoy Nikolay Kudashev said that there is "ample scope" for cooperation between India and Russia on Afghanistan and both sides have been in regular touch with each other on the latest developments in the war-torn country.
He also said that Russia is as concerned as India that the Afghan soil should not be a source of spreading terrorism to other countries and there is a "danger" of terror being spread to the Russian territory as well as Kashmir.
The Russian ambassador also said that there is not much difference in the overall position of Russia and India on Afghanistan and noted that Moscow's approach in according recognition to a Taliban regime would depend on its actions.
With PTI inputs