"The phone conversation addressed the intensive efforts being exerted to implement recent understandings [between Israel and Gaza-based resistance factions] in hopes of ending the Gazan people's suffering", the statement read.
On Friday, Israel extended the fishing zone to 12 nautical miles, after a ban for six days.
Both the Erez crossing for passengers and Karm Abu Salem crossing for goods were opened and are now operating in accordance with the previously established mechanisms and timelines.
A United Nations (UN) fact-finding mission found earlier that Israeli forces committed rights violations during their crackdown against the Palestinian protesters in Gaza that may amount to war crimes. Their visit follows last weekend's flare-up in fighting, which killed 29 Palestinians, over half them civilians, and four Israeli civilians.
This week's demonstrations were seen as a key test for a fragile truce agreed between Gaza's Islamist rulers Hamas and Israel.
A Palestinian was killed by Israeli fire at a weekly demonstration along the Gaza-Israeli border fence, according to Palestinian officials.
Israeli authorities have long imposed unilateral restrictions on Palestinian fishermen in the Gaza Strip, which are routinely enforced with violent attacks by naval vessels.
On May 15, protest organisers are calling for a massive border march to mark the 71st anniversary of what Palestinians call the "Nakba", or catastrophe, when hundreds of thousands of Palestinians fled or were forced from their homes in the 1948 war that led to the establishment of Israel.