TEL AVIV, Israel - Israel on Monday began administering a third shot of the Pfizer/BioNTech coronavirus vaccine to patients with compromised immune systems, as cases in the country rise, the health ministry said.

Those immediately eligible for a third shot include people who have had heart, lung and kidney transplants and some cancer patients.

"There is accumulating evidence that patients with immunosuppression do not develop an adequate antibody response after two doses of the vaccines," a health ministry statement said.

It added that the decision to give a third dose was spurred by the rising daily case tally.

Israel's initial vaccine rollout of the Pfizer/BioNTech jab was among the world's fastest, and it succeeded in bringing confirmed daily cases down to single digits last month.

With more than 85 percent of the its adult population fully inoculated, Israel had removed all its pandemic containment restrictions, restoring indoor dining and removing caps on large gatherings.

But the emergence of the Delta variant -- first identified in India in April -- has led to a surge in transmission, with several hundred new infections now recorded daily.

Experts have said there are clear signs the vaccine is less effective in preventing mild illness against the Delta variant.

Sheba Medical Center in Tel Aviv said it will give a third shot to several heart-transplant patients on Monday.