In Jerusalem, police and border police patrolled areas around the Western Wall and major shopping areas.
The Israeli military usually closes Israel's borders with the West Bank and Gaza over the New Year holiday, when packed synagogues, beaches and parks in Israel are seen as being vulnerable to attack.
However, this year there will be no closures.
The New Year, Rosh Hashanah, lasts for two days and begins at sundown on Sunday. The ten days between the start of Rosh Hashanah and Yom Kippur is a period of soul searching for Jews, known as the "Days of Awe."
At the lively open-air Mahane Yehuda market in central Jerusalem, shoppers scrambled to stock up on food before the two-day holiday as Israeli police looked on.
Security also remained visibly high at Israel's borders with Gaza and Egypt on Sunday, following a wave of angry protests in the region over an anti- Islam film.
Muslims angry over the film produced in the US denigrating the Prophet Muhammad took the streets on Friday in more than 20 countries from the Mideast to Southeast Asia.
In most countries, protests were peaceful, if vehement. But deadly clashes erupted in several places.
