He appeared to suggest that it was more than just an issue related to deliveries from a production centre in India.
Speaking on BBC CWR (Coventry and Warwickshire), he said: “The production for AstraZeneca in the UK has been excellent…but again that also needed to scale up which is happening.
“We depend on their obviously global supply chain as well and that has been a little bit slower to come through.
“Pfizer are doing really well.”
Reports suggests that the slowdown in supplies to the UK is due to a delay in getting five million doses from the Serum Institute in India.
However, Mr Zahawi appeared to point to it being a broader issue. “It’s not shortage of supply from India or elsewhere. AstraZeneca is a global production and supply chains in vaccines are global,” he said.
He stressed that the Government was still on target to offer a first dose to all over 50s by mid-April and also by the end of July for all adults to have had at least one dose.
The two vaccine manufacturers both said they remained on course to meet delivery commitments, denying any disruption to supplies.
Vaccination centres and community pharmacy-led services were told to close unfilled bookings and “ensure no further appointments are uploaded” to booking systems next month.
NHS bosses said that as a result of the supply issues, people under the age of 50 should only get the jab if they are in a priority group, meaning younger adults could face a longer wait.
But a Pfizer spokeswoman said deliveries “remain on track” for the first quarter of its 40 million dose agreement with the UK, with a “steady supply of vaccines” delivered to the nation.
Meanwhile, an AstraZeneca said in statement: “Our UK domestic supply chain is not experiencing any disruption and there is no impact on our delivery schedule.”
But Labour’s shadow health secretary Jonathan Ashworth urged Mr Hancock to explain what the reported supply issues were and how the Government was aiming to resolve them.
“Trying to dismiss or downplay the legitimate concerns of anxious people waiting for a vaccine is simply not good enough,” Mr Ashworth added.
Asked about the letter, Mr Hancock said: “Supply is always lumpy and we are on course to deliver the offer that everybody who is aged 50 and above will be able to get vaccinated by the 15th of April. I recommit to that today.
“And, of course, these supply schedules have moved up and down throughout this whole rollout. It’s absolutely par for the course and that’s a normal operation letter.
“We are committed to all adults being able to get the jab by the end of July and we are on track to deliver on that commitment.”
The European Commission chief said she wanted “reciprocity and proportionality” in exports, pointing out that 10 million doses of vaccine had gone from the EU to the UK.
Mr Hancock said the supply of vaccines to the UK from EU production facilities was “fulfilling contractual responsibilities and we fully expect those contracts to be delivered on”.