Israel took a step towards normalcy on Sunday, re-opening a raft of businesses and services from pandemic lockdowns, but with some only available to fully vaccinated "green pass" holders.  

Nearly three million people, almost a third of Israel's population, have received the two recommended doses of the Pfizer/BioNTech coronavirus vaccine, the world's quickest inoculation pace per capita.

With a steady flow of data proving the Pfizer vaccine's efficacy in stopping serious illness from COVID-19, Israel's government has begun gradually easing restrictions in place since December, when it imposed its third lockdown.

Shopping malls and stores with street access re-opened Sunday, with certain limitations on crowd size. 

But gyms, swimming pools, hotels and some cultural facilities are re-opening only to those who have been fully vaccinated and obtained the so-called green pass. 

Israel's green pass scheme is being closely watched as a possible model for how other economies might re-open once a substantial part of the population is vaccinated, while stirring controversy over unequal access for those who opt out of the jab. 

Lifting weights at a gym in Petah Tikva near Tel Aviv late Saturday, Prime Minister Benjamin Netanyahu insisted Israel was moving ahead "with caution", while imploring "everyone to get vaccinated".

Standing at the entrance of a posh Tel Aviv gym, 90-year-old Ora Davidovicz said she "couldn't wait" to go swimming. 

"It's been almost a year since I went to the pool," she told AFP. "I've been counting the days.

"All I have to do is put on my swim suit," she said, before heading in. 

Tom John, a muscular 33-year-old, told AFP he'd been training at home for months but felt safe being back at the gym with the protection systems in place.  

"Everyone here has a green badge," he said, surveying the gym. 

- 'The right' re-opening -

As of Sunday, nearly 3.2 million Israelis were eligible for the green pass, according to the health ministry.  

That includes 2.5 million people who had their second shot more than a week ago, as well as nearly 700,000 people who have recovered from COVID-19. 

At the family owned Katalina shoe store in central Tel Aviv, Mordechai Nazarian said his business had been closed for eight of the last 12 months, with "little openings here and there" as Israel lifted restrictions between lockdowns. 

"We hope this one is the right one," he told AFP.

At the Third Ear record store in Tel Aviv, 32-year-old Itay Shimon said he hadn't been in a record store in many months, but was enjoying just browsing the aisles. 

Describing himself as a vaccine supporter, he also voiced caution about compelling people to get the jab.

"We cannot force those who don't want it to do it," he said.

Israel, which has one of the world's most sophisticated medical data systems, secured a substantial stock of the Pfizer/BioNTech vaccine by paying above market price and by striking a data-sharing deal with the drug giant.

Netanyahu is hoping the successful vaccine procurement and rollout will boost his support ahead of March 23 elections, Israel's fourth vote in less than two years.