Jaishankar said he was confident that Prime Minister Modi and President Putin will meet for an annual summit next year.
Russian Foreign Minister Sergey Lavrov and Defence Minister Sergey Shoigu will visit India to hold the inaugural '2+2' ministerial dialogue between the two countries on December 6, the Russian embassy has said.
'Pleasure to meet FM Sergey Lavrov, this time in person. Excellent talks that reflect our Special and Privileged Strategic Partnership. Value our exchanges on the international situation,' Jaishankar tweeted after talks with his Russian counterpart on the sidelines of the SCO meeting.
At a media briefing, French President Emmanuel Macron said the G20 leaders' declaration "confirms" Russia's isolation for its attack on Ukraine and that the bloc is committed to "just and lasting" peace in the war-torn country.
At a joint media briefing with Lavrov, Jaishankar listed issues such as "factors of instability" such as terrorism and its cross-border manifestation and said it remains a "major concern".
It is learnt that Lavrov is expected to travel to India either on Thursday or Friday after concluding a two-day visit to China.
India has been in touch with all parties concerned as part of overall global efforts to bring down the tensions.
He may have spent his entire adult life in diplomacy, but doctorate in nuclear physics Subrahmanyam Jaishankar's face betrays both fusion and fission of his moods.
The US move to align with Russia is prompted by fear of a Sino-Russian joint threat. Russia, fully aware of its military vulnerability vis a vis China may cautiously welcome the American move, assesses Colonel Anil A Athale (retd).
The high-level talks took place in the backdrop of indications that India could buy greater volumes of discounted Russian oil and both sides were keen on having a rouble-rupee arrangement for bilateral trade.
G20 leaders, including United States President Joe Biden, United Kingdom Prime Minister Rishi Sunak and United Nations Secretary General Antonio Guterres, paid tributes to Mahatma Gandhi at his memorial Rajghat in New Delhi on Sunday.
New Delhi has reached out to Moscow while waiting for a new president in Washington. New Delhi knows well that in international relations, there are no permanent friends or foes, only permanent national interests, points out Dr Rup Narayan Das.
Russian Foreign Minister Sergey Lavrov said Moscow sees the prospect of making the Security Council more democratic, exclusively, through broadening the representation of countries from Africa, Asia and Latin America.
'He may respect others, but he is unlikely to admire them'
Russia on Thursday ruled out playing a role in resolving the Kashmir problem, saying India and Pakistan are capable of settling their outstanding issues themselves.
EAM Jaishankar's mission is aimed at strengthening India's strategic autonomy in a complex international environment, observes Ambassador M K Bhadrakumar.
The summit is being attended by more than 30 heads of state and top officials from the European Union and invited guest countries and 14 heads of international organisations.
Chinese and Russian warplanes on Tuesday conducted joint air patrols over the Sea of Japan, the East China Sea and the West Pacific Ocean as the leaders of Quad held their in-person summit in Tokyo, in an apparent attempt to send a message of unity between Beijing and Moscow.
Russian President Vladimir Putin on Tuesday thanked Prime Minister Narendra Modi for trying to help find a peaceful solution to the Ukraine crisis.
The foreign ministers of India, Russia and China on Friday held discussions on key regional and international issues, including situation in Iran, North Korean rocket launch and terrorism during a trilateral meet in Moscow.
Russian Foreign Minister Sergey Lavrov, who was representing President Vladimir Putin, left Bali on Wednesday, a day ahead of the scheduled conclusion of the G20 Summit held amid the economic challenges triggered by the Russia-Ukraine war.
Prime Minister Narendra Modi and President Vladimir Putin held the 21st India-Russia summit, covering an array of areas with an aim to further enhance the special and privileged strategic partnership between the two countries.
Foreign Secretary Harsh Vardhan Shringla on Wednesday had 'fruitful and productive' meetings with top Russian diplomats on bilateral issues as well as regional and global issues of mutual interest and the two sides discussed ways to further strengthen the bilateral Special and Privileged Strategic Partnership.
Locked in a fierce battle with the Georgian troops, Russian security forces on Saturday bombarded key military bases in the breakaway South Ossetia province for the second straight day as Moscow claimed that 1,500 people were killed in fighting in the sensitive region.
Earlier this week, Guterres had written to Putin and Ukraine's President Volodymyr Zelenskyy to receive him in Moscow and Kyiv 'to discuss urgent steps to bring about peace in Ukraine'.
Kamboj's stern response to Pakistan came in her remarks at the UN Security Council open debate on "Maintenance of international peace and security: Effective multilateralism through the defence of the principles of the Charter of the United Nations" chaired by Russia, President of the Council for the month of April.
"Reports of PM Modi not meeting Putin due to nuclear threat is baseless. The meeting is not taking place due to scheduling issues," sources told ANI.
The leaders were accompanied by US Secretary of State Rex Tillerson and Russian Foreign Minister Sergey Lavrov at the bilateral meeting.
In his opening remarks at the talks, Defence Minister Rajnath Singh asserted that India is confident of overcoming the challenges with a strong political will and an inherent capability of its people.
Prime Minister Narendra Modi on Saturday welcomed a host of world leaders, including United States President Joe Biden and United Kingdom Prime Minister Rishi Sunak, at the Bharat Mandapam, the venue of the G20 Summit.
Delhi's appeasement strategy may now translate as more mega arms deals with the US, generating substantial business and job creation in the American economy. Make no mistake, Americans will use it to pressure India, predicts Ambassador M K Bhadrakumar.
Russian Foreign Minister Sergey Lavrov on Wednesday warned that a third World War, should it break out, will be "nuclear and devastating", amid spiralling tensions with the West over Moscow's ongoing massive military operation against Ukraine.
Taking to Twitter, the ministry shared the intelligence update and said, 'Russian forces have continued their advance on Kyiv with the bulk of their forces now 30km from centre of the city.'
External Affairs Minister S Jaishankar is in Moscow on a four-day visit to attend the meeting of foreign ministers of the SCO of which both India and China are members.
Russia proceeds "from the postulate, a negotiated solution to the Palestinian-Israeli conflict has no alternatives," said Putin while speaking at the Commonwealth of Independent States summit in Bishkek, Kyrgystan on Friday.
The highly anticipated historic G20 Leader's Summit begins on Saturday, September 9, in New Delhi.
The Modi government finds itself in a contradiction of its own making. It has encouraged pro-Russian, Westophobic public sentiment while setting strategic policy that's exactly the opposite, points out Shekhar Gupta.
The development comes following the third round of talks between Russia and Ukraine in Belarus on Monday, which apparently ended up in failure.
Jaishankar said he emphasised that India supports diplomacy and dialogue as the "way out".
"We foresee a very intensive engagement during the day that will culminate in the summit," the MEA spokesperson said.