His official spokesman said on Tuesday: “We don’t have surplus doses."
India's health system has been overwhelmed by surge in COVID infections, with the country recording 320,000 new cases and 2,771 reported deaths on Tuesday alone.
When asked if vaccines will be sent to the country, Johnson’s spokesman said: “We committed in February to sending excess doses from the UK’s supply to the COVAX procurement pool and to countries in need once they are available.
“Right now we are moving through the UK prioritisation list for our domestic rollout and we don’t have surplus doses, but we will keep this under review.”
It comes a day after defence secretary Ben Wallace said "we’ll do everything we can to alleviate their [India's] suffering".
According to Oxford University's Our World in Data website, the UK has administered 68.72 doses per 100 people, compared to 10.33 per 100 in India.
Watch: India receives first batch of UK-funded COVID aid
While the government has ruled out sending vaccines to India – where the crisis has overwhelmed the country’s health services – it has sent medical supplies.
The first of nine plane-loads of life-saving kit, including 200 ventilators and 95 oxygen concentrators, arrived in New Delhi early on Tuesday.
The equipment will be sent to Indian hospitals, with further consignments due to be dispatched later this week, including another 400 oxygen concentrators.
Foreign secretary Dominic Raab tweeted: “Good to see the first of our medical supplies have now arrived in India and will be deployed where they are needed most.
“No one is safe until we are all safe. International collaboration is key to fighting this global threat.”
Meanwhile, Joe Biden’s White House was moving to share raw materials for the AstraZeneca vaccine by diverting some US orders to the Serum Institute of India.
However, questions about sharing doses are likely to continue during India's crisis, particularly given the UK's successful rollout of the vaccine.
Jabs were being offered to people aged 42 and over on Tuesday, with the government aiming to have offered a first dose to every adult by the end of July.
In January, the UK committed £548m to the COVAX initiative, which aims to help distribute 1.3 billion doses to 92 developing countries this year.
However, that programme has struggled, with the Guardian reporting last week how it has only delivered about one in five of the Oxford/AstraZeneca doses that it had estimated would arrive in countries by May.
Earlier this year, meanwhile, Dr Tedros Adhanom Ghebreyesus, director-general of the World Health Organization (WHO), also warned a “me first” approach would prolong the pandemic and human and economic suffering.
Watch: Should the UK share its vaccines with India?