The letters were exchanged after the election of Shehbaz as prime minister early this month but both the sides kept development away from the media glare in what seemed to be a move aimed at avoiding any public attention, The Express Tribune newspaper reported.
Citing a senior Foreign Office official, the paper said that Putin wrote to Sharif, congratulating him on his election.
He also expressed desire to deepen cooperation between the two countries.
In his reply, Shehbaz expressed similar sentiments on bilateral ties between the two countries as well as cooperation on Afghanistan, it stated.
The exchange of letters between the two leaders took place as former prime minister Imran Khan is adamant that he was ousted from power through an alleged US-backed vote of no-confidence since Americans did not like his Russian policy.
Washington has strongly refuted Khan’s claims.
Khan travelled to Russia in February where he held talks with Russian President Vladimir Putin and the two leaders reviewed the entire array of bilateral ties including energy cooperation besides exchanging views on major regional and international issues.
His visit coincided with the start of a special military operation by Russia in eastern Ukraine.
Khan, a cricketer-turned-politician, was the first Pakistani premier to visit Russia in 23 years after former premier Nawaz Sharif travelled to Moscow in 1999.
Khan has said that the powerful military was onboard over his visit to Russia and he telephoned Chief of Army Staff General Qamar Javed Bajwa before the visit.
On April 12, the Russian Embassy in Islamabad, through Twitter, congratulated Prime Minister Shehbaz and expressed hope that ties between the two countries would grow under his government.
The new regime in Islamabad is pushing to reset ties with the West, particularly the US that have strained considerably following Khan’s rhetorical statements, the report added.
Pakistan’s ties with Russia have moved past the bitter Cold War hostilities in recent years and the chill in the relations between Pakistan and the US has further pushed the country towards Russia and China.
The two countries are not just exploring options to deepen economic ties, but Russia is also keen to sell arms to Pakistan, something it avoided in the past because of India’s opposition.
Pakistan and Russia have already been holding regular joint military exercises since 2016 in another sign of deepening ties between Moscow and Islamabad.
They also share the same view on key regional and international issues, including Afghanistan.