Israeli Defense Minister Benny Gantz spoke with Palestinian President Mahmud Abbas over the phone on Tuesday on the occasion of the Muslim holy month of Ramadan, Gantz's office said.
"Minister Gantz wished (Palestinian Authority) Chairman Abbas and the Palestinian people a blessed month of Ramadan," the statement said.
"Ramadan must be a month of peace and quiet and not a period marked by terror," Gantz told Abbas, according to the statement, pointing to recent deadly attacks in Israel.
Last year during Ramadan, clashes that flared between Israeli forces and Palestinians visiting occupied east Jerusalem's Al-Aqsa mosque compound led to 11 days of devastating conflict between Israel and the Gaza Strip's Hamas rulers.
"Israel is prepared to expand civilian measures during and after the month of Ramadan, in accordance with the security situation," Gantz added, according to AFP. The statement did not elaborate on the measures that would affect Palestinians.
He also expressed "appreciation" for Abbas' comments on an attack in the town of Bnei Brak near Tel Aviv late last month.
The Palestinian president had issued a rare condemnation of the March 29 attack in which five people were killed after a Palestinian opened fire at passers-by, saying that the killings "will only lead to further deterioration of the situation, while we are all striving for stability".
A total of 11 people have been killed in attacks in Israel since March 22, including some carried out by assailants linked to or inspired by ISIS.
Over the same period, eight Palestinians have been killed, according to an AFP tally, including two assailants in anti-Israeli attacks and six people the Israelis said had carried out attacks or were about to do so.