Sharif told this to Russian President Vladimir Putin when they met for the first time on the sidelines of Shanghai Cooperation Organisation (SCO) Summit in Ufa.
According to an official statement, Sharif told Putin that Pakistan attached great importance to its relations with Russian Federation.
"He informed President Putin that Pakistan is keen to enhance its relations with the Russian Federation and wants a multi-dimensional relationship with Russia in the fields of trade, defence, energy, infrastructure, culture and other spheres," the statement said.
The two sides expressed confidence that the meeting would help in raising the level of friendship and cooperation between the two countries.
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President Putin congratulated the Prime Minister on the launching of formal accession of Pakistan to SCO.
He stated that Russia attaches importance to its relations with Pakistan and would like to further enhance them, particularly in the economic domain.
Both leaders reviewed the progress in a number of projects under consideration especially in the energy sector and expressed satisfaction on the progress being made in finalising North-South gas pipeline agreement and decided to expedite the process.
Once Cold War-era adversaries, relations between the two countries are improving after 40-years of hostility during which Pakistan was in the anti-Soviet Union camp and had been instrumental in the Soviet pullout from Afghanistan in 1980s.
Pakistan and Russia last year also signed a military cooperation agreement to deepen their defence ties and vowed to translate their relationship in "tangible" terms during the first-ever visit of a Russian defence minister in 45 years.
Russian Defence Minister Shoigu's visit last November to Pakistan came at a very critical juncture as US-led NATO forces drawdown from Afghanistan.