President al-Sisi was called by Prime Minister Netanyahu about Saturday's deadly violence on the normally calm border, the spokesman for the Egyptian president said.
During the conversation, the two leaders stressed "the importance of coordination between the two countries to clarify the circumstances", he said.
Egypt has said the policeman crossed into Israel while chasing drug smugglers, leading to exchanges of fire with Israeli soldiers.
Earlier, Netanyahu called the Egyptian shooter a "terrorist" although he has since mostly spoken of the shootings as an "incident."
President al-Sisi offered Netanyahu his "deep condolences," the Israeli prime minister's office said.
On Tuesday, his office said he had "thanked the Egyptian president for... his commitment to an exhaustive and joint investigation of the incident."
"The two leaders expressed their commitment to further strengthening peace and security cooperation, which is an essential value for both countries," it added.
Questions have been raised about why the Egyptian assailant - reported by Egyptian media to have been a 22-year-old conscript - crossed into Israel and opened fire.
Speaking at the opening of a cabinet meeting on Sunday, Netanyahu said his government had sent a "clear message" to Egypt: "We expect that the joint investigation will be exhaustive and thorough."
Israel's border with Egypt has been largely quiet since Egypt became the first Arab country to make peace with Israel following the Camp David accords of 1978.
In recent years, there have been exchanges of fire between smugglers and Israeli soldiers stationed along the border.
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