Some patients are waiting days to have their prescriptions filled, with many community pharmacies struggling to meet demand during lockdown.
Pharmaceutical Society president Ian McMichael said there had been a massive increase in workload.
"Pharmacies are run off their feet because there's a huge need, people can't see their GPs and it's all falling back on pharmacies to provide for people."
Many pharmacies, like his own in Hamilton, had introduced split shifts to ensure they could keep operating if someone became ill.
This meant there were fewer staff working at any one time.
"Our phones just aren't stopping, and also at this time we're doing lots of vaccinations, and we've got it blocked off so people can't directly coming into the pharmacy, so staff are doing lots of running backwards and forwards.
"So we've got fewer staff and more work to do."
Supply chain hiccups due to Covid-19 had made more work for pharmacists, he said.
"Every time there's a supply issue of us not being able to hand out medication or there not being enough, we've got to ask them to come back, which we don't want - or we've got to send it out to them, which is a cost to us."
Some were having to ask patients with non-urgent prescriptions to return in a couple of days to pick up their medicines.
McMichael said the government "deserved full credit" for its $15 million cash injection to help pharmacies support high-needs patients during lockdown.
But more work was needed to ensure vulnerable people - particularly the elderly, Māori and Pacific people - did not miss out.
"There's also some real issues around ongoing disease management for people that have got nothing to do with Covid-19, and not being able to get access to medical care, hospital care or their pharmacies particularly well."
The chairperson of the Medical Association's GP council, Jan White, was disturbed at reports that patients were turning up at hospitals with heart attacks at a later stage.
She said people needed to know their family doctors were still there for them.
"Getting in early with heart attacks and stroke symptoms, we must continue to do that. The patients must contact us and the service is there for them.
"It's just being delivered in a slightly different way."
Dr White, who works in a central Auckland practice, said pharmacies were under pressure but there were no complaints.
"I have had feedback from the pharmacist closest to us that they've been absolutely overwhelmed and running around crazily trying to fulfil everything, but I've certainly had no negative feedback from patients."
Pharmac director Lisa Williams said the agency was doing its best to listen to what pharmacies needed on dispensing rules and stock management to make their jobs easier.
"Like us, pharmacists understand that Covid-19 is likely to have global impacts on medicine manufacture and supply chains for the remainder of 2020 and potentially beyond.
"While we are working with our suppliers to minimise any impacts on the supply chain and manufacturing disruptions caused by the various shutdowns, we have also considered how we can help our community pharmacists face any supply issues."
Pharmac was encouraging pharmacists to use their discretion and dispense larger supplies of medicines to those who are immunocompromised, elderly or have underlying health conditions, she said.
- If you have symptoms of the coronavirus, call the NZ Covid-19 Healthline on 0800 358 5453 (+64 9 358 5453 for international SIMs) or call your GP - don't show up at a medical centre
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