India reported 211,298 new infections on Thursday, the world's highest daily rise, but almost half the daily infections it recorded earlier this month.
Pfizer officials and the government also discussed the indemnity protection against liabilities and asked for relaxation in some clauses before the company brings its COVID-19 vaccines to India, the sources said.
The government said it was in talks with Pfizer for "earliest possible" imports of its shots and that it had also had discussions with Johnson & Johnson and Moderna.More news: Facebook Reverses Course, Won't Ban Lab Virus Theory
Only about 3% of India's 1.3 billion people have been fully vaccinated, the lowest rate among the 10 countries with the most cases.
But experts believe that figure grossly underestimates the actual toll as only people who have tested positive are counted, whereas many victims were never tested.
"We have spoken to Pfizer and Moderna for vaccines, and both the companies have refused to sell vaccines directly to us".More news: Vancouver Island adds 9 new COVID-19 cases
"The provision has now been further amended to waive the trial requirement altogether for the well-established vaccines manufactured in other countries", the government said in a statement. "They have said that they will deal with the Government of India alone", Delhi Chief Minister Arvind Kejriwal had said on Monday. "Now for most people, we will be moving it up to about eight weeks".
Seeking a fast-track approval for its COVID-19 vaccine, US major Pfizer has told Indian authorities that its jab has shown "high effectiveness" against the SARS-CoV-2 variant prevalent in India and on people of Indian ethnicity or nationality, while it is suitable for everyone aged 12 years or above and can be stored for a month at 2-8 degrees, sources said on Wednesday. India has also been using two vaccines - Covishield by the Serum Institute of India (SII) and Covaxin by the Hyderabad-based Bharat Biotech.
There was no immediate response from Pfizer, Moderna or Johnson & Johnson to Reuters requests for comment.More news: European Union to cut air links with Belarus following flight diversion incident
William Shakespeare, the first man in the world to get an approved Covid-19 vaccine, died in the University Hospital Coventry and Warwickshire aged 81 after suffering a stroke.