"It is in the interest of the Palestinian people not to give Israel any pretext to continue its aggressions," a statement from the Palestinian leader's office said.
Against the backdrop of apparent IDF preparations to embark on a large-scale operation in Gaza, Abbas called Israel's threats to target the Strip "dangerous."
"(Abbas) demands that Israel halt its attack and demands that all factions adhere to immediate calm and to stop the firing of rockets," the statement said.
Army hits Hamas targets
Meanwhile, the US State Department urged Israel to "consider the consequences" of any action and Middle East envoy Tony Blair said everything must be done to avoid "even more victims of the situation created in Gaza."
However, despite the calls tensions remain high around the Strip while the heightened level of violence that has plagued the region in recent days continued Friday.
The Palestinians fired more than 15 rockets at southern Israeli communities throughout the day, including a rocket that landed near a group of Yisrael Beiteinu Knesset members who toured the area.
Meanwhile, Friday evening the IDF renewed its strikes on Gaza and targeted a Hamas arms production site in the center of the Strip, as well as a rocket launcher in northern Gaza. The army said that that the targets were hit in both strikes, but no injuries were reported.