Israeli Prime Minister Benjamin Netanyahu said in a speech on Monday that "all citizens must be alert".
Israeli authorities have arrested dozens of Palestinians after a deadly shooting rampage in Jerusalem raised fears of a surge in violence during this week's Yom Kippur holiday, police said Monday.
Sunday's attack saw a 39-year-old Palestinian open fire on civilians from a car and at police, killing a police officer and a 60-year-old Israeli woman.
The attacker, Misbah Abu Sbeih, who was reportedly scheduled to begin a prison term on the same day, was killed by police after he fled into an east Jerusalem neighbourhood.
The shooting came at a time of increased Jewish visitors to the flashpoint Al-Aqsa mosque compound in Israeli-annexed east Jerusalem for the holidays of Rosh Hashanah, which was last week, and Yom Kippur, which begins Tuesday evening.
The same increase typically occurs for the Jewish Sukkot holiday that takes place next week.
The site is holy to both Muslims and Jews, who refer to it as the Temple Mount.
Tens of thousands of Jews also visit the nearby Western Wall during the holidays.
Last year's Jewish high holidays led to clashes and marked the start of an upsurge in Palestinian gun, knife and car-ramming attacks.
Hundreds of police to deployThe arrests included 31 Palestinians seeking to participate in celebrations in memory of the assailant as well as members of his family in east Jerusalem, Public Security Minister Gilad Erdan told army radio.
Abu Sbeih's 17-year-old daughter, who had posted a video widely shared on social media networks in which she praised her father and his deeds, was among those arrested, Palestinian media said.
"God willing my father will be our patron on judgement day and we will all go to heaven thanks to my father," said Eiman Abu Sbeih in the video.
A family member told AFP she was remanded into custody for an additional three days.
Some 15 other Palestinians were arrested for throwing stones and Molotov cocktails at security forces in east Jerusalem, police spokeswoman Luba Samri said.
The military said it has also made preparations to demolish the home of the attacker, a practice Israel often employs in a bid to deter others from violence.
In addition, police are increasing deployments throughout Israel and Jerusalem for the holidays, with more than 3,000 to be deployed to the city.
Israelis have been concerned that the attack may inspire copycats.
The use of a sophisticated rifle, reportedly an M-16, also led to worries as it was a departure from the more typical use of knives or homemade guns.
Hamas, the Islamist movement that runs the Gaza Strip, welcomed the attack and said the assailant was a member, but did not claim responsibility.
Israeli Prime Minister Benjamin Netanyahu said in a speech on Monday that "all citizens must be alert".
"We know that this is a time when those who fan the flames of terrorism and the inciters try to ignite a conflagration," he said.
Abu Sbeih, was from the Silwan area of east Jerusalem, located just outside the Old City and near Al-Aqsa.
He was known as an activist for the "defence" of the holy site and was said to have belonged to an informal group of Muslims, called the Mourabitoun, dedicated to the cause.
Banned Al-Aqsa group
Israel banned the group last year, accusing it of inciting hate.
Palestinian media said Abu Sbeih was due to begin a four-month prison term on Sunday for attacking an Israeli police officer in 2013.
Violence since October 2015 has killed 232 Palestinians, 36 Israelis, two Americans, one Jordanian, an Eritrean and a Sudanese national, according to an AFP count.
Most of the Palestinians killed were carrying out attacks, according to Israeli authorities.
Others were shot dead during protests and clashes, while some were killed in air strikes on the Gaza Strip.
Many analysts say Palestinian frustration with the Israeli occupation and settlement-building in the West Bank, the complete lack of progress in peace efforts and their own fractured leadership have fed the unrest.
Israel says incitement by Palestinian leaders and media is a leading cause of the violence.
The vast majority of the attacks have been carried out by lone-wolf assailants, Israeli authorities say. Many have been young people, including teenagers.