In an unusually quick response even as counting of votes was underway in Pakistan, Singh conveyed India's desire to work with him to chart a new course in Indo-Pak relations.
"The Prime Minister has extended his congratulations to Sharif and his party for their emphatic victory in Pakistan's elections," the PMO said in a statement here.
Singh invited Sharif to visit India at a "mutually convenient time".
Singh also congratulated the people and the political parties of Pakistan for braving the threats of violence and voting in large numbers.
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The PML-N returned to power after millions of Pakistanis braved Taliban threats and violence that claimed some 50 lives to vote in the landmark general election that marked the first transition from one civilian government to another in the country's 66-year history.
External Affairs Minister Salman Khurshid hoped that India will continue to have good relations with Pakistan under Sharif's leadership.
Sharif served as premier during 1990-1993 and 1997-1999 but was ousted from office before he could complete his term - once on corruption charges and later because of the coup led by Musharraf.