The meeting took place in response to a request by the Indian Prime Minister for a courtesy call on the President en route to the nearby Prime Minister House for the traditional 'Retreat' of the Saarc leaders.
The meeting, according to Indian External Affairs Minister Yashwant Sinha, lasted a little less than an hour, while Foreign Office spokesman Masood Khan said it went slightly beyond 60 minutes.
Both Sinha and Masood seemed to be very happy over the meeting, in which the two leaders were accompanied by aides.
On Pakistan side were present Foreign Minister Khurshid Kasuri, Finance Minister Shaukat Aziz, who is Minister-in-Waiting to the Indian Prime Minister, Foreign Secretary Riaz Khokhar and High Commissioner Aziz Ahmed Khan.
Vajpayee was accompanied by Yashwant Sinha, Indian National Security Adviser Birjesh Mishra and Foreign Secretary Shashank.
Both Sinha and Masood declined to entertain questions about the controversial issues which have plagued the relations between the two neighbours since Independence.
They rather advised the questioners to avoid questions, which might prove harmful to the present harmonious climate.
When a questioner drew his attention to an electronic media report quoting Information Minister Sheikh Rashid Ahmed that the two leaders had discussed substantive issues which also included Kashmir, Sinha firmly refused to go beyond the few lines of a written statement he had read about the meeting.
When other journalists insisted to know what exact topics were raised at the meeting, Sinha said he would not like to speak further on the subject. "Anything more will not be in the interest of the cause for which the summit was taking place," he added.
Sinha, however, departed from his firm stance when he said that his Prime Minister had not been invited to visit Pakistan. A curt "no comment" was his answer to a question on the meeting Indian National Security Adviser Birjesh Mishra was reported to have earlier in the morning with the Chief of Pakistan's Inter-Services Intelligence agency. "I am not in a position to say anything," he added.
In reply to another question whether Musharraf and Vajpayee had a one-to-one meeting, Sinha said the aides continued to be present during the meeting.
A statement read by Pakistan Foreign Office spokesman a few hours after Sinha was almost the same as given out by Indian External Affairs Minister.
It said: "The Prime Minister of India, Mr Atal Behari Vajpayee, paid a courtesy call on the President of Pakistan. The meeting took place in a cordial atmosphere.
"The Indian Prime Minister thanked the President of Pakistan for the excellent arrangements made for the Indian delegation and the hospitality extended to them. He also congratulated the President on a very successful conduct of the 12th Saarc Summit.
"The two leaders discussed the positive impact of the recent confidence-building measures and hoped that their momentum would be maintained.
"The meeting lasted for slightly more than an hour. From the Indian side, the External Affairs Minister, the National Security Adviser and the Foreign Secretary attended the meeting.
"Form the Pakistan side, the Foreign Minister, the Finance Minister, the Foreign Secretary and our High Commissioner in India were present.
On the sidelines of the Saarc Summit, the Indian Prime Minister had requested for a call on the President. Accordingly, the meeting took place today."
Sources said the Indian Prime Minister refused to budge from his government's stated position.
India found the confidence-building measures, announced by Pakistan, so far helpful but stressed that more needed to be done, sources said. Resumption of dialogue at the official levels, as asked by Pakistan, was also not agreed to by the Indian leader.
Indian hesitation to take a clear position on resumption of dialogue was forcefully reflected in the remarks by Vajpayee at India High Commission function some time ahead of his meeting with President Musharraf.
"New questions have come up for which new answers have to be sought," was what he said.
When asked if the Musharraf-Vajpayee meeting could be taken as resumption of dialogue, the FO spokesman's reply was: "Positive development is that Prime Minister Vajpayee has met (our) prime minister and president. We hope it would facilitate dialogue."
He said: "We have these positive meetings. This is just the beginning." He said he thought the "present process" would culminate into a "composite dialogue".
From Pakistan's perspective the big success is that the 12th Saarc summit has taken place and, on top of that, it brought about the Musharraf-Vajpayee meeting. But, quite conspicuous by its absence was any mention in on-the-record remarks or statements by the two sides of the United States for any role it played to facilitate the bilateral contact in Islamabad.
However, the presence of Prime Minister Vajpayee's National Security Advisor Berjish Mishra in Islamabad has evoked curiosity. The FO spokesman had "no information" if he met DG, ISI. But then he made the cryptic remark: "Mishra is part of Indian delegation and is meeting with officials. It is no big deal."
Unlike the Indian Minister, the Foreign Office spokesman fielded all sorts of questions at his 40-minute meeting with the media but side-tracked all controversial issues - in a humorous and polite way.
The Summit will conclude on Tuesday morning with the signing of the 'Islamabad Declaration' and farewell speeches by the participating leaders. After a joint news conference by new Saarc Chairman Zafarullah Khan Jamali and Secretary-General QMA Rahim, the visiting leaders will leave for home.
APP adds: To a question whether the issue of oft-repeated Indian allegation of "cross-border terrorism" figured in the talks, Yashwant Sinha said, "I can't share the details."
He said the meeting between President Musharraf and Prime Minister Vajpayee was not one-on-one and aides from both the sides attended the meeting.
FO spokesman Masood Khan said: "The meetings are a process - we have to invest in these and (these) will have a positive impact on peace and security in the South Asian region".
To a question about more meetings between the leaders of the two countries, Khan said "our first priority is to resume dialogue", but, added that the future meetings have not been decided.
About the meeting between Prime Minister Vajpayee and President Musharraf, Khan said: "These meetings are significant because this is the first contact between the leaders of the two countries since Agra."
Responding to a question, he said, Pakistan hopes that the present process that is underway will culminate in a composite dialogue and will include discussion on all outstanding issues including Kashmir.
He replied in affirmative when asked about the possibility of nuclear Confidence Building Measures (CBMs) in future and said this is a long-term goal. This is their responsibility that they should elaborate CBMs and come up with a restraint regime".