"The UK is deeply concerned by the growing violence and civilian casualties and we want to see an urgent de-escalation of tensions," Mr Johnson said in a short statement posted on social media on Wednesday morning.
Renewed clashes began on Friday when more than 200 Palestinians and 17 Israeli police officers were hurt in Jerusalem.
Thousands of worshippers had gathered at the city's al-Aqsa mosque for their weekly Friday prayers and were attacked by police with rubber bullets and stun grenades.
The show of force by Israeli authorities was in response to Ramadan protests over police restrictions in the Old City and the threatened eviction of dozens of Palestinians from their homes in the Sheikh Jarrah neighbourhood.
The violence quickly escalated, with Hamas militants firing rockets into Israeli territory and Israel responding with airstrikes.
43 people, including 13 children, have been killed by Israeli airstrikes, while Hamas rockets have killed five.
Speaking in the House of Commons Layla Moran, the Liberal Democrats' foreign affairs spokesperson, read the names of some of the children who had been killed in the strikes, as she asked an urgent question to ministers.
"My heart breaks for them – and Mr Speaker my heart bleeds for Palestine, for Jerusalem, the city of my family, for the worshipers attacked by extremists in the al-Aqsa mosque on the holiest night of Ramadan and for all innocent civilians, Israeli and Palestinian. We cannot allow this to escalate any further,” she said.
"The Israeli government pursuing evictions in Sheikh Jarrah that would be illegal under international humanitarian law including the fourth Geneva Convention, and the subsequent overly aggressive reaction of the Israeli authorities that injured hundreds has ignited a tinder-box. And Hamas then retaliated and those strikes must be condemned too because violence only begets more violence."
She added: "If this isn't the time to recognise the state of Palestine, then when is? The United Kingdom has a historic responsibility to the people of Palestine and a fundamental obligation to uphold international law. That two-state solution as promised to the likes of my family is as elusive as ever. It is time for the government to not just say, but do."
James Cleverly, the Foreign Office minister for the Middle East, said in response to Ms Moran's urgent question: "The UK unequivocally condemns the firing of rockets at Jerusalem and other locations in Israel. We strongly condemn these acts of terrorism from Hamas and other terrorist groups, who must permanently end their incitements and rocket fire against Israel. There is no justification for any targeting of civilians.
"Israel has a legitimate right to self-defence, and to defend the citizens from attack. In doing so, it is vital that all actions are proportionate, in line with international humanitarian law, and make every effort to avoid civilian casualties. Violence against peaceful worshipers of any faith is unacceptable.
"UK has been clear that the attacks on worshipers must stop. The status quo in Jerusalem is important at all times, but especially so during religious festivals, such as Ramadan. Our priority now must be an immediate deescalation of all sides, and an end to civilian deaths.
"As I made clear over the weekend we are concerned about tensions in Jerusalem, linked to threatened evictions of Palestinian families from our homes ... that threat is allayed for now, but we urge Israel to cease such actions which in most cases are contrary to international humanitarian law."
Speaking after the parliamentary exchange Lib Dem Ms Moran said: “Last night, the UN Special Envoy to the Middle East Peace Process warned that the situation in Israel and Palestine is 'escalating towards a full scale war'.
“It is therefore vital that the UK Government plays our full part through international diplomatic efforts to call for de-escalation, now, today. One would hope that that could be through the Security Council but we also cannot wait for the United States.
“I have serious concerns regarding the willingness of the UK Government to follow these steps, concerns which have not been allayed by the Minister’s response to my Urgent Question."
She added: “The Foreign Secretary’s media statement on the crisis focused solely on Hamas, making no acknowledgment of the role of the Israeli government. Neither was there any recognition of the provocative timing of these attacks, during Ramadan. It is vital that, along with full de-escalation, international pressure is put on both the Israeli government and Hamas to abide by their commitments under international law.
“The UK must do all it can to avoid war. What we need now is the full force of the international community to say: this has to stop. And it’s not just the Israeli government that has to stop. The escalation of the rocket fire towards Israel must cease. We need people to put down their arms - to stop killing innocent civilians, and children - and get back to the negotiating table.”
Later on Wednesday Downing Street backed Mr Cleverly’s approach. Asked whether Mr Johnson agreed with apparently stronger criticism of Hamas rockets, a spokesperson said: “We are 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.”
Asked whether the PM would specifically condemn Israeli actions, the spokesperson said: “We condemn the civilian casualties as simply unacceptable and we want both sides to step back from the brink.”
He added: “We are clear there can be no justification for terrorist attacks on civilians. The Prime Minister has made his position clear on that. We do not condone the killing of innocent civilians under any circumstances.”
The spokesperson declined to comment on government minister Zac Goldsmith’s retweet of a message from the Israeli Defence Force which stated that “no country on Earth would be expected to tolerate these incessant attacks on innocent civilians by an organisation committed to their total eradication”.
Labour leader Keir Starmer said on Wednesday afternoon: “The situation in Jerusalem, Gaza and Israel is shocking. Labour is calling for the immediate end to air strikes and rocket attacks. Britain must act to de-escalate tensions and kick-start efforts for a sustainable peace - through a two-state solution.”