Addressing a meeting of newly elected PML-N lawmakers in Lahore, Sharif said Zardari had not yet congratulated him on the success of the party.
Soon after, Zardari telephoned Sharif and felicitated him on his victory in the May 11 general elections, presidential spokesman Farhatullah Babar said.
Media reports quoted sources close to Sharif as saying that the PML-N chief asked Zardari what had taken him so long to offer the congratulations.
The PML-N has attained a simple majority in the National Assembly or lower house of parliament, setting up an unprecedented third term as premier for Sharif.
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Zardari's Pakistan Peoples Party, which led the previous government, was routed in the polls.
Zardari also telephoned Jamiat Ulema-e-Islam chief Maulana Fazlur Rehman and Awami National Party head Asfandyar Wali, the presidential spokesman said.
The President felicitated the people and all political parties for participating in the elections, paving the way for the first democratic transition in the country's history.
Babar quoted Zardari as saying that the polls followed by the smooth transfer of power in the coming days "will be remembered as a watershed mark in our political evolution and a triumph of the democratic ethos of the people and the political parties".