Vajpayee said he would restore full diplomatic ties with Pakistan, including the return of an Indian ambassador to Islamabad, and reopen travel links between the neighboring nations.
"How long will we keep fighting with Pakistan? We want to give Pakistan one more chance, not out of weakness but out of self-confidence," Vajpayee told parliament.
"The third attempt will be decisive and will be the last in my lifetime," he said.
The 78-year-old Vajpayee led two unsuccessful rounds of peace talks with Pakistan in 1999 and 2001 in attempts to end a decades old conflict between the countries, rooted in a dispute over ownership of the divided region of Kashmir.
India cut all air and rail links and withdrew its ambassador from Islamabad after an attack on the Indian parliament in December 2001 that was blamed on Pakistan-based militants. Pakistan denied any involvement in the incident.
India later massed thousands of extra troops along its border with Pakistan, leading the two nuclear-armed countries to what many diplomats viewed as the brink of war.
"We are committed to the improvement of relations with Pakistan and we are willing to grasp every opportunity for doing so," Vajpayee told the Indian lawmakers.
Last week, Vajpayee conditionally offered new talks with Pakistan on the disputed Kashmir region and other issues, according to the Associated Press. Pakistani President Gen. Pervez Musharraf expressed some reservations, but called the overture a sign of improvement.
Pakistani officials appeared to welcome the new moves by India on Friday.
"Pakistan is ready to start a dialogue process so as to hold meaningful discussions on all outstanding issues between the two countries including that of Jammu and Kashmir," Pakistan's Foreign Minister Mian Khursheed Mehmood Kasuri told a news conference.
Kasuri also welcomed Vajpayee's decision to return an official diplomat to Islamabad saying that Pakistan would also upgrade diplomatic relations.
Pakistan's Prime Minister Zafarullah Khan Jamali is expected to give the formal reply to India's offer of new dialogue, although the exact contents of the country's official response are unknown.
U.S. Secretary of State Colin Powell congratulated the countries on taking what he called "first steps" toward improving relations. Washington has been pushing the two to reduce tensions and start new talks.
"I am very pleased with developments on the subcontinent over the last several weeks," Powell told reporters in Albania during his current tour of Europe and the Middle East. "I understand there have been some additional openings and we are on the verge of seeing representatives return to each others capitals."
"All this is very, very promising at a time when we were beginning to wonder whether or not we were not going back to the potential of conflict," he said.
U.S. Deputy Secretary of State Richard Armitage is due to visit the region next week.