Mr Jamali responded to a call for talks by Mr Vajpayee
Pakistan's Prime Minister Zafarullah Jamali has invited his Indian counterpart Atal Behari Vajpayee to Islamabad in what is being seen as a breakthrough in relations.
He made a 10-minute telephone call to Mr Vajpayee in a move his officials say has ended an 18-month impasse.
Correspondents say it was the first high-level contact between the nuclear-armed neighbours since they came to the brink of war last year.
The disputed territory of Kashmir lies at the heart of disagreement and has been the flashpoint for two of three wars between India and Pakistan since partition.
Pakistan's Foreign Minister, Khurshid Mahmud Kasuri, welcomed Monday's phone call, and told the BBC a new war would be "devastating" for both countries.
"It's quite obvious that war is not the solution," he told The World Today.
Mr Vajpayee made an offer of talks last week during a landmark speech in Indian-administered Kashmir - the first by an Indian prime minister in the Muslim-dominated Kashmir valley for 16 years.
His speech was seen as a test to see whether progress could be made over Kashmir - and whether it would be accepted by hardline members of Mr Vajpayee's party.
Mr Jamali took up the initiative and responded by inviting Mr Vajpayee to Islamabad for a meeting at a time of his choosing, officials said. He said he would be happy to make a reciprocal visit.
A Pakistani Government statement said: "The telephone call breaks the 18-month-old impasse between the two countries.
India accuses Pakistan of fomenting militants in Kashmir
"The two prime ministers also exchanged views on exploring ways and means to initiate relations in economic, cultural and sports fields," it added.
The BBC's Zaffar Abbas in Islamabad says it is not clear whether the 10-minute phone call will lead to immediate progress.
But he says it will reduce tensions between the two countries which stationed one million troops facing each across the common border last year.
Delhi has continued to accuse Islamabad of aiding militants seeking to overthrow the Indian administration in part of Kashmir.
Pakistan denies that charge and says it does all it can to seal the border on its side of the disputed territory.