Sameh Shoukry called for a two-state solution, but said conditions for achieving it were deteriorating.
His trip is seen as a sign of strengthened ties between two countries sharing deep concerns over regional unrest.
Israeli PM Benjamin Netanyahu has said he welcomes Egypt's efforts.
The last round of peace talks between Israel and the Palestinians came to an end amid acrimony in April 2014.
The Palestinians accused Israel of reneging on a deal to free prisoners, while Israel said it would not continue negotiations after the Palestinians decided to bring the militant Islamist Hamas movement into a unity government.
Mr Shoukry, the first Egyptian foreign minister to visit Israel in nine years, said the current state of affairs was "neither stable nor sustainable".
He added that the vision of two states living side by side was "not far-fetched" and called for confidence-building measures that could lead to renewed peace talks.
"It is no longer acceptable to claim that the status quo is the most that we can achieve of the hopes and aspirations of the Palestinian and Israeli peoples," he said, alongside Mr Netanyahu in Jerusalem.
Mr Shoukry met the Palestinian Authority President, Mahmoud Abbas, in the West Bank on 29 June.
Co-operation between Israel and Egypt has intensified under Egyptian President Abdul Fattah al-Sisi.
Egypt faces Islamist militants in the Sinai region south of Israel, and both countries are wary of Gaza's Hamas Islamist rulers.
In May, Mr Sisi urged both sides to seize the opportunity to make a peace deal, offering the Arab peace initiative of 2002 as a potential way ahead.
Mr Netanyahu said he would be willing to discuss the plan, but that changes would have to be made.
He repeated his call for Palestinians to resume direct negotiations with Israel.
Violence has escalated recently, and 35 Israelis have been killed in a wave of knife, gun and car-ramming attacks since October.
More than 200 Palestinians - mostly attackers, Israel says - have also been killed in that period.
Earlier this month, the so-called Middle East Quartet said ongoing violence, Israeli settlement-building and Palestinian splits were undermining peace hopes.
And it warned of "perpetual occupation and conflict" between both sides.
Egypt's foreign minister has paid a rare visit to Israel, offering his country's help to revive peace talks with the Palestinians.