"If anyone doesn't believe in Indian Constitution, then why should anyone talk to them?," said Congress leader Digvijay Singh.
Another party leader and former Union Minister Anand Sharma said the Modi government should adopt a coherent and consistent approach to engage in talks with Pakistan.
"Talking about our neighbours, with Pakistan or China, relationships which are sensitive, complex and sometimes there have been areas of concern, have to be integral to the foreign policy. That is why I said it has to be consistent; it has to be a roadmap.
Veteran BJP leader LK Advani said India will not tolerate if someone goes against it. "And whatever understanding we have with you (Pakistan) , you will have to respect our position."
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CPI(M) leader Sitaram Yechuri felt the situation might "worsen" given the "signals" Pakistan was sending and the way Centre was responding.
National Conference said dialogue was for reconciliation but the Centre needed to determine what will be the contours of the same.
"Dialogue is essential for any reconciliation. However, when, how and where dialogue takes place nd what will be the contour of the dialogue has to be decided by India," Devendra Singh Rana said.
India had called off foreign secretary-level talks with Pakistan last year after Basit held consultations with Hurriyat leaders on the eve of the official talks.
Last night Basit had met Mirwaiz Umar Farooq along with Abdul Gani Bhat, Maulana Abbas Ansari, Bilal Gani Lone, Aga Syed Hassan, Mussadiq Adil and Mukhtar Ahmad Waza and invited them to today's Pakistan National Day celebrations here.