The meeting comes on the heels of the gunning down of the key Mumbai blasts suspect, Nasir, in an encounter on Friday.
Advani asserted that if his party is returned to power in the next general elections then it would scrap the deal and renegotiate with the US government.
The leader of opposition in Lok Sabha drove to prime minister's official residence after a breakfast meeting with Lok Sabha Speaker Somnath Chatterjee.
Vajpayee was elected chairman of the BJP parliamentary party.
The way things have gone and the way the Shankaracharya has been treated, the people and the nation are concerned."
He denied that his demand marked a departure from his party's original stand that the deal was unacceptable because of Washington's Hyde Act.
Around 11,500 Pakistanis have come into India with regular papers, but have overstayed. There is no reason to be soft on them, he said.
"Last time I had gone there, I was told that the Americans also feel equally angered about December 13 attack and this time I am going to take up further incidents of terrorism that occured in the country," the deputy PM said.
"I have seen several MPs who do not speak a word (in Parliament) and yet are elected repeatedly," the Leader of Opposition and senior BJP leader said.
The announcement came a day after Hurriyat chairman Maulvi Abbas Ansari expressed willingness to hold the talks if the Centre extended an invitation.
The deputy PM referred to an article written by actor Amitabh Bachchan extolling the new, resurgent India.
The special court hearing the demolition case fixed May 31 for the next hearing.
This business of them [BJP leaders] going to the press with every little thing must stop, the UP chief minister said.
Bharti's stay at Amarkantak since April 3 had given rise to a variety of speculations.
Bharatiya Janata Party leader Lal Kishenchand Advani congratulated Bharatiya Janata Party's three MP's -- Ashok Argal and Faggan Singh Kulaste from Madhya Pradesh and Mahavir Baghora from Rajasthan -- who exposed Congress MP Ahmed Patel's attempt to buy them to stay away from the trust vote.
In a letter to Prime Minister Manmohan Singh, Bharatiya Janata Party leader Lal Kishenchand Advani has requested the government to honour former Prime Minister and senior BJP leader Atal Bihari Vajpayee with the Bharat Ratna, the country's higest civilian honour.
She said she would hand over her resignation to Governor Balram Jhakar on Monday.
"Indeed, the effort to bring about a rapprochement in India-China relations was initiated when Atal Bihari Vajpayee was the foreign minister in Morarji Desai's government. His historic meeting with Deng Xiaoping in 1979 broke the ice and resumed top-level dialogue that had been frozen since the 1962 Indo-China war. Shri Vajpayee also gave a big boost to this effort when he became the Prime Minister," he said.
"It is an internal matter. We will meet and sort out the issues," Advani told the weekly BJP parliamentary party meeting.
The Rashtriya Swayamsevak Sangh on Monday night said it will extend its support to Bharatiya Janata Party veteran Lal Kishenchand Advani, who was projected as party's prime ministerial candidate, while National Democratic Alliance allies like Janata Dal-United and Shiv Sena reserved their comment.
CBI counsel S S Gandhi, however, said the CBI had, 'oral evidence' against all the eight accused persons, including Advani, M M Joshi and Uma Bharti.
The right-wing outfit also accused the Centre of working on a deal to abandon the Kashi and Mathura temple issue.
The Uttar Pradesh unit of the BJP is unhappy with the Mayawati government using the anti-terror law against jailed independent MLA Raghuraj Pratap Singh.
Deputy Prime Minister L K Advani said the dialogue would later be extended to other sections who did not participate in the assembly election or did not get elected.
While the papers had mentioned that Advani would arrive at 3 pm the cops said that he would arrive at 4 pm. Among the 1,500 strong crowd there were less than 50 women. Local leaders kept the crowd occupied.
"Unfortunately today dynasty has become an issue. When people tell me that she (Pratibha) should be in politics. I oppose it because it's an issue on which we always confront the principal ruling party in the country," he said in an interview to television channel NDTV in Delhi, which also featured his daughter Pratibha.
Both leaders should take note of their age and remove themselves from active command of the party, RSS chief K S Sudarshan said.
Though no major accord is likely to be signed between the government and the insurgent outfit, the high-level parleys are expected to pave the way for the launch of a political process involving the NSCN (I-M).
He was hinting at the Hurriyat Conference, which said it is ready for talks with the government on the Kashmir issue if it is allowed to visit Pakistan to talk to militant groups there.
Advani and Dr Joshi might not attend the consecration ceremony due to health and age-related reasons. Advani is 96 and Dr Joshi will turn 90 next month.
Deputy Prime Minister Lal Kishenchand Advani conveyed this to Bharatiya Janata Party general secretary Pramod Mahajan.
Leader of Opposition L K Advani moved the motion.