Around 50 people, including 13 children, have now died in the worst violence in the region since the 2014 war in Gaza.
Hundreds more rockets were fired into Israel by Palestinians militants in Gaza overnight, mostly targeted at Tel Aviv, while Israeli air strikes brought down two tower blocks in Gaza.
Meanwhile the city of Lod, near Tel Aviv, has been put under a state of emergency amid rioting.
Mr Johnson said he was “deeply concerned” by the violence and casualties, calling for an urgent “de-escalation” of tensions.
The PM said: “I am urging Israel and the Palestinians to step back from the brink and for both sides to show restraint.
“The UK is deeply concerned by the growing violence and civilian casualties and we want to see an urgent de-escalation of tensions.”
It comes as Tor Wennesland, UN Special Envoy to the Middle East Peace Process, warned that Israel was heading “towards a full-scale war”.
He tweeted: “Stop the fire immediately. We’re escalating towards a full scale war. Leaders on all sides have to take the responsibility of de-escalation.
“The cost of war in Gaza is devastating and is being paid by ordinary people. UN is working with all sides to restore calm. Stop the violence now.”
The latest fighting comes after violent confrontations between Israeli police and Palestinian protesters at a major holy site and tensions over a plan to evict dozens of Palestinians from an East Jerusalem neighbourhood.
Tensions boiled over on Monday, with Hamas firing rockets at Israel which responded with airstrikes on what it said were “military targets”.