The report did not provide more details about the conversation on Thursday.
Barlev later tweeted that he hopes to open lines of communication with Palestinian counterparts in the interest of peace and security for the two peoples, reports Xinhua news agency.
"That friendly conversation is the first of its kind between an Israeli internal security minister and the president of the Palestinian Authority," the Minister said.
On Monday, Palestine's official WAFA news reported that Abbas received phone calls from his Israeli counterpart Isaac Herzog and Defence Minister Benny Gantz.
Herzog congratulated Abbas on the occasion of the Muslim holiday of Eid al-Adha.
Gantz wrote on Twitter that he spoke with Abbas to express "well wishes on the occasion of Eid al-Adha" and "discussed the need to advance steps of trust-building between us".
The Israeli-Palestinian peace talks have stalled since April 2014 due to their deeply-rooted disputes over the settlements, security and borders.
Ramallah, July 23
Palestinian President Mahmoud Abbas held a phone conversation with Israeli Minister of Public Security Omer Barlev to discuss peace and security issues in the region, an official media report said.
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