Mr Singh met Russian President Vladimir Putin on Monday as the two countries agreed to boost cooperation in defence, trade, security and energy sectors.
India was expected to sign a key deal on seeking Russia's help in setting up two nuclear plants in Kudankulam in the southern state of Tamil Nadu.
The deal did not go through but Delhi and Moscow agreed to iron out issues in the near future.
"In a bid to overcome legal hitches that have held up a deal on two new plants at the Kudankulam nuclear power complex over liability provisions, India and Russia pledged to 'resolve all outstanding issues' related to the project even as they decided to elevate their strategic ties to new levels in defence and other area," says a report published in The Economic Times.
India's liability law stipulates that nuclear firms aiming to set up plants in India will have to pay huge sums of money in case of an accident.
But the failure to sign the deal has not affected cordial ties between the two nations and their leaders.
The two also agreed to boost cooperation in fighting global terrorism.
"Both sides affirmed the need to join efforts of all states to defeat terrorism. They condemned terrorism in all its forms and manifestations and agreed that there should be no tolerance for sheltering, arming, training or financing of terrorists," a joint Russia-India statement says.
Indian newspapers are also highlighting Mr Singh's statement in which he said "no country has had closer relations with India and no country inspires more admiration, trust and confidence among the people of India than Russia".
In a gesture marking their close friendship, Russian President Vladimir Putin Monday presented visiting Indian Prime Minister Manmohan Singh a lithograph painting of Russian monarch Nicholas II who had visited India in the 19th century, a map of India of that time as well as a Mughal coin.
The "very special gesture" of the Russian president "went beyond protocol" as no one had an inkling of it. The Russian president had personally got the items, said Indian Ambassador Ajai Malhotra to reporters here at a briefing.
Not only did Putin present Manmohan Singh with the gifts, he also explained the significance of the items, said the envoy.
Putin recalled the history of the early 1900s and the attempt by the tsar to open a Russian consulate in India.
The Russians had first applied to open a diplomatic mission in Bombay in 1857, but the British rulers were not helpful. Nicholas had visited 30 Indian cities during his trip.
The Mughal coin showed the close trade ties that India and Russia have shared for ages, said the envoy.
Putin's gifts were aimed to showcase how India-Russia ties were part of history, he added.