Israeli Defence Minister Benny Gantz wished Palestinian leader Mahmoud Abbas "a blessed Ramadan" during a phone call on Tuesday.
"Ramadan must be a month of peace and quiet and not a period marked by terror," Mr Gantz told Mr Abbas, referring 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 rulers Hamas.
"Israel is prepared to expand civilian measures during and after the month of Ramadan, in accordance with the security situation," Mr Gantz said on Tuesday.
The statement did not reveal measures that would affect Palestinians.
Mr Gantz expressed "appreciation" for Mr Abbas's comments on an attack in the town of Bnei Brak near Tel Aviv late last month.
The Palestinian leader 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 the ISIS group.
During the same period, eight Palestinians have been killed, an AFP tally shows, including two assailants in anti-Israeli attacks and six people the Israelis said had carried out attacks or were about to do so.