Jamali asked Vajpayee to resume negotiations with Islamabad, offered to visit India "in the cause of peace," and urged the two archenemies "to resolve outstanding issues through dialogue," according to Pakistan Television.
Tensions have been high between the South Asian neighbors, who have fought two of their three wars over the disputed Kashmir region, which is divided between India and Pakistan but which both claim in its entirety.
So far India has refused negotiations with Pakistan, demanding Islamabad first end cross-border infiltration into Indian-ruled Kashmir by Muslim militants, who have been fighting since 1989 for the region's independence or merger with Pakistan.
Pakistan says it is doing all it can to seal the border and has asked for an increase in international monitors to verify New Delhi's claim.
During the conversation Jamali told Vajpayee he welcomed his original offer of talks. Vajpayee made the offer during a visit last week to the troubled Indian-Kashmir capital of Srinagar.
However, Vajpayee qualified the offer, saying Pakistan had to close training camps for militants and end cross-border infiltration. Pakistan denies involvement in either.
Islamabad says it only gives political and moral support to the militants.
The dispute over Kashmir attracted international attention only after India tested a nuclear device in 1998 and Pakistan followed with a test of its own. Both countries have declared themselves nuclear powers and there are fears that another conflict could escalate into a nuclear confrontation.