Vaccination centres will remain open through the Eid holiday, he said.
Anyone over the age of 75 should go to the nearest vaccination centre and did not need to book in advance, Dr Abdulaali said.
More than 10.5 million vaccine doses have been administered in the country of about 30 million people.
Saudi Arabia reported 942 Covid-19 infections and 13 deaths from the virus on Sunday.
“There is fluctuation in the coronavirus curve in Saudi Arabia and we hope it will decline as it did in the past,” Dr Al Abdulaali said.
The Interior Ministry said there had been 25,672 breaches of the country’s precautionary measures over the past seven days.