The federal government launched its vaccine booking system on Wednesday leading to a sudden flood of calls to doctors' clinics whose details were shared online.

KRS Health is one of four Wagga practices named among more than 1000 Australian clinics approved to immunise eligible patients from Monday.

Practice manager Kristy Wilson said "every second phone call" since Wednesday morning had been from people asking about the vaccine, but the clinic still didn't have a concrete date for its availability.

"We don't even have our vaccines yet. We're actually telling our patients to call us back on Monday," she said.

"We have been given a date of the 22nd yes, but there have been reports that the vaccines haven't arrived on time."

The Murrumbidgee Primary Health Network has named Blamey Street Surgery, Kooringal Medical Centre and Glenrock Country Medical Practice as the other Wagga general practices able to administer the vaccine, but Glenrock has been left off the government's online portal.

Blamey Street Surgery practice manager Julie Manton said she expected their first shipment of vaccines to arrive on Friday.

"We're not taking bookings until we actually have the vaccines. People can phone and we'll put them on the waiting list," she said.

Murrumbidgee Primary Health Network acting chief executive Julie Redway said the initial rollout of Phase 1b would offer the vaccine locally in 10 towns across the region.

"Over the coming weeks, more of our general practices will commence vaccinations, and we will keep you informed of these," she said.

Tumut health advocate Colin Locke, aged in his 70s, said he would be "putting my hand up" to get vaccinated but said he would wait to see if any of his local GPs could administer it.

The Snowy Valleys are currently in a vaccination blackspot, with the nearest available GP clinics listed on the government's vaccine portal located in Wagga or Canberra.

"That's not a suitable outcome. If the federal government is serious about this they should give the authority to the state government who then uses a proper mechanism through the health system," Mr Locke said.

Federal Health Minister Greg Hunt defended the rollout on the ABC's AM program this morning, saying he was grateful for the public's interest in the vaccination program when asked about GPs being swamped with calls.