Sharif invited Singh to Pakistan on Monday, Express News reported adding he said he would also invite Singh to his oath-taking ceremony.
Nawaz has already indicated his desire to normalise "roller-coaster" ties with India.
Prime Minister Singh had yesterday lost no time in congratulating Sharif on his election victory, which will give him his third term as prime minister of Pakistan, and invited him to visit India at a mutually convenient time.
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.
In a letter to Sharif, prime minister Singh said, "I look forward to working with you and your government to chart a new course and pursue a new destiny in the relations between our countries. I would also like to extend an invitation to you to visit India at a mutually convenient time."
During the campaign, 63-year-old Sharif had vowed to revive the Indo-Pak peace process which was interrupted in 1999 by the then military ruler Parvez Musharraf who ousted him in a bloodless coup. Sharif had started the peace process with then Prime Minister Atal Bihari Vajpayee.
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