Rehman Malik shocker: Don't know whether Kargil martyr Captain Saurabh Kalia died of Pakistan bullet or weather
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President Asif Ali Zardari had already invited Singh to visit Pakistan, Malik told the media before leaving for Delhi.
"I would also invite the Indian Prime Minister for a visit on behalf of our leadership," he said.
Malik is visiting the Indian capital for the operationalisation of a new visa agreement signed by the two countries in September.
He described the visa accord as a gift from the leadership of both countries to future generations as peace and stability between the two sides would usher in a new era of progress and development.
People from India and Pakistan, especially senior citizens, businessmen, traders and journalists, can easily visit both countries to further enhance trade and cultural relations, he said.
Malik claimed his visit to India was a "victory for peace and those who wanted to see an improvement in Pakistan-India relations".
He said that during his visit, he would give message to the world that Pakistan and India are peace-loving nations that believe in coexistence and want to live as peaceful neighbours.
Earlier in the day, Indian High Commissioner Sharat Sabharwal met Malik ahead of his visit to Delhi.
Malik and the Indian envoy discussed "bilateral relations and matters of mutual interest", Pakistani officials said.
They also discussed the new visa pact.
Ahead of Malik's arrival in Delhi, External Affairs Minister Salman Khurshid said India had seen "little progress" as far as accountability by Pakistan for the Mumbai attacks is concerned.