Councillor Andy Morgan tweeted an invite to locals of all ages to visit Bolton's vaccine bus.
Bolton has become a hotspot for the new variant, which is spreading rapidly.
The Scientific Advisory Group for Emergencies (Sage) concluded there is a “realistic possibility” the strain is 50% more transmissible than the one that emerged in Kent.
If the variant is more transmissible lifting restrictions could “lead to a substantial resurgence of hospitalisations” that is “similar to, or larger than, previous peaks”, Sage said.
In the tweet Mr Morgan said that the vaccine team would "find a reason" to give attendees the jab.
"Anyone with a Bolton Postcode & registered with a Bolton GP can visit the vaccine bus at the @EssaAcademy vaccination site and #GetVaccinated", he wrote.
"The team will find a reason to vaccinate you. Closes at 5pm. The 4000 vaccines must be used today."
It follows a number of new measures to combat the spread of the virus
On Friday Prime Minister Boris Johnson announced that people aged over 50 and the clinically vulnerable will have their second doses of a Covid vaccine accelerated.
Mr Johnson warned that the variant could cause “serious disruption” to plans to ease the lockdown and may delay the planned ending of all legal restrictions on June 21.
Surge testing is also under way in several places in England including areas of Bolton, Blackburn, Sefton and London.
Public Health England data shows a rise in cases of the Indian variant of concern from 520 to 1,313 this week in the UK.