Vajpayee called for a 'conducive atmosphere' for talks
South Asia's two nuclear rivals, India and Pakistan, are to re-establish full diplomatic relations.
Prime Minister Atal Behari Vajpayee told the Indian parliament he would restore full Indian diplomatic representation in Islamabad.
Hours later Pakistan announced it would reciprocate.
The threat of war between the two traditional enemies has caused huge concern since an attack on the Indian parliament in December 2001.
The moves were welcomed by US Secretary of State Colin Powell, who congratulated the two countries for taking what he called very promising first steps to peace.
UK Foreign Secretary Jack Straw said he hoped they would be the cue to "normalising" relations between India and Pakistan, and pledged Britain's continuing support.
PM's 'last effort'
"It has been decided to appoint a high commissioner to Pakistan and to restore civil aviation links on a reciprocal basis," Mr Vajpayee said in his parliamentary address.
"We are committed to the improvement of relations with Pakistan and are willing to grasp every opportunity for doing so."
There have been a series of attacks in Kashmir recently
However, on the possibility of talks to resolve the Kashmir dispute, Mr Vajpayee said that there would be no role for any "third-party" to mediate, a long-standing demand of Pakistan.
Mr Vajpayee, now 78, said this, his third attempt to settle differences with Pakistan, "will be decisive and will be the last in my lifetime".
In Islamabad, Pakistani Foreign Minister Khursheed Kasuri welcomed the move.
"Pakistan wants high commissioner (ambassador) relations with India," he said according to the Associated Press news agency.
On Monday, Pakistani Prime Minister Zafarullah Jamali used a phone call with Mr Vajpayee to invite him to Islamabad.
The BBC's Sanjeev Srivastiva in Delhi says
Mr Vajpayee is unlikely to accept that invitation in a hurry, as India-Pakistan summit meetings in recent years have failed to take the peace process much forward.
The emphasis this time around seems to be on a more graded and cautious approach, with both Delhi and Islamabad apparently agreeing on initiating official level discussions first to prepare the ground for a possible meeting of the two prime ministers later this year.
Dec 2001: India recalls its envoy after parliament attack
May 2002: Pakistan envoy expelled after attack on Indian army camp
Feb 2003: Deputy ambassadors of both countries expelled after a row over Kashmiri separatist funding
Friday's diplomatic moves mark a dramatic change in atmosphere after a long period of heightened tension that saw the US leading outside attempts to prevent war breaking out.
India reacted with fury after armed gunmen attacked the federal parliament in Delhi in December, 2001.
It blamed the attack on Pakistan-based militants it said were supported by the government in Islamabad.
Pakistan denied the accusation.
The ensuing months saw India deploy huge numbers of troops along their common border, with Pakistan responding in kind.
There have been a number of signs recently that India and Pakistan are willing to take steps to address their differences, particularly over the Kashmir dispute.
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If funding from the West to separatists is stopped, the Kashmir issue will die
But Mr Vajpayee made clear to parliament that he was not withdrawing India's long-standing demand for the Pakistan Government to stop allowing militants to infiltrate into Indian-administered Kashmir.
"We have repeatedly expressed the need to create a conducive atmosphere for a sustained dialogue which necessarily requires an end to cross-border terrorism and the dismantling of its infrastructure," he said.
Pakistan denies giving militants such support.
India and Pakistan have fought two of their three wars over Kashmir.