The sudden move to drop Abbas for the post in New Delhi was the fourth change in less than a month with regard to the posting of envoys in key world capitals.
Abbas' "agreement" (formal consent for posting) had been sought from the Indian government. A fresh request for consent will now be send to the Indian side.
Basit was tipped for the post of Foreign Secretary last month to replace Jalil Abbas Jilani, who has been named as the new Ambassador to the US.
Foreign Office spokesman and Additional Foreign Secretary Aizaz Chaudhry, who was set to go as the envoy to Belgium and the European Union, is now expected to be made Foreign Secretary.
Basit earlier served as a Director General during 2008-09 and as Additional Secretary (Europe) during 2009-12. His last posting was as the envoy to Germany.
Current High Commissioner Salman Bashir had been asked to continue in New Delhi for Punjab Chief Minister Shahbaz Sharif's visit to India last week.