Ipswich MP Tom Hunt told Education Secretary Gavin Williamson that schools in the town were ready to vaccinate staff - and had people with the right skills to do the job themselves.
Mr Hunt, who is a member of the Education Select Committee, told Mr Williamson: "I have a school in my constituency which is working with other schools that feels it has the facilities and also the trained staff to vaccinate all of the local teaching staff in the area.
"So it would simply be a matter of getting them the vaccine and they'd be able to get on with it without taking anything away from the wider vaccination strategy."
Ipswich MP quizzes Education Secretary on the role schools c
His comments came during a meeting of the committee which was asking the Education Secretary about how his department was dealing with the current lockdown and the Covid crisis.
The need to vaccinate school staff - support staff as well as teachers - was near the top of the agenda for most MPs.
Mr Williamson responded to Mr Hunt saying it had to be up to the Joint Committee on Vaccination and Immunisation to decide who should get the jabs first.
He added: "My priority is to see teachers, support staff, to be the place to get the vaccine at the very earliest moment and I agree with you, I think there is a real appetite and a real ability that schools can play a major role out in not just the testing but also in terms of vaccination."
Mr Hunt is the second Suffolk MP to tackle Mr Williamson on vaccinations - last month South Suffolk MP James Cartlidge urged the government to say school staff should be considered as a priority.
He said this would allow schools to reopen more safely - and also give teachers and support staff the confidence to return to work without having to worry about the virus.
He said: "It is the adults at schools who are more at risk from suffering serious symptoms of Covid-19 and this would enable schools to be able to continue operating with more confidence if there is an outbreak."
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