New Zealand has started to relax its strict lockdown, with residents able to travel to work, spend more time outside and order takeaway food for the first time in more than four weeks.

The move from level 4 measures to level 3 came as Jacinda Ardern, the prime minister, was forced to clarify that her country had not eradicated Covid-19 but was working towards its elimination.

On Monday a number of international publications ran prominent headlines that New Zealand was the first country in the world to eradicate the disease, after what were regarded as confusing comments by the government.

On Tuesday Ardern said: “Elimination does not mean zero cases, it means zero tolerance for cases.”

Community transmission had ceased, she said, but isolated cases would continue to pop up and would continue “being stamped out” until a vaccine was found. Scientists were working on a vaccine overseas and domestically but a mass roll-out was thought to be at least a year away, she said.

Dr Ashley Bloomfield, the director general of health, said “elimination is not a point in time” but something that would have to be consistently worked on.

“We haven’t eradicated the virus,” Dr Bloomfield said. “But we have achieved what we wanted to achieve in our ongoing goal of elimination.”

Epidemiologists advising the government on the elimination strategy said the virus should be treated like measles, with the appearance of any cases treated as dangerous and requiring a strong public health response including rigorous contact tracing.

Schools around the country will open on Wednesday but the prime minister said very few children were expected to attend, as she was advising anyone who could work from home or study from home to do so.

Roads and streets were busier under level 3 and a limited number of cafes and restaurants opened to customers, either using delivery apps or putting small tables out the front of their premises for customers to collect food and coffees – which were in particular demand.

Queues for fast-food such as McDonald’s began forming at dawn, and pizza delivery shops such as Dominos hired thousands more workers to meet demand.

“It’s hard to explain how good this tastes,” Christopher Bishop, a member of parliament, said on Twitter after posting a picture with a takeaway coffee.

New Zealand has reported 1,122 confirmed cases of Covid-19 up to Tuesday, including 19 deaths, one of the lowest tallies in the world, while 82% of all confirmed and probable cases had recovered, and nine people were being treated in hospital – one in ICU.

“We can say with confidence that we do not have community transmission in New Zealand. The trick now is to maintain that,” Ardern said, describing level 3 as “the waiting room”.

New Zealand is maintaining several social distancing policies with malls, pubs, hairdressers and other public shopping areas to stay shut for at least another two weeks.

Siouxsie Wiles, a microbiologist and associate professor at the University of Auckland, was among those warning the virus could return if lockdown measures were eased too quickly or not adhered to by the public.

“If we turn our backs for a minute, we’ll be on the path to a serious outbreak once again. And we’ve seen this happen overseas,” Wiles wrote in a column for The Spinoff.

Not everyone was happy with the end of level 4. On social media some said the peace of the mornings had been disturbed by the sound of traffic and they could no longer hear birds calling to one another, while others were disturbed by the swift return of consumer culture.