President Barack Obama is urging Israelis and Palestinians to restrain themselves and put an end to acts of retribution in the recent round of violence.
Mr Obama’s article comes as militants in the Gaza Strip responded with rocket attacks to Israeli aristrikes.
Israel carried out more airstrikes on the Gaza Strip in apparent retaliation to the dozens of rockets fired by the Palestinian group Hamas.
The military urged Israelis within a 24-mile radius of the territory to stay within reach of protected areas.
At least 15 Palestinians, including two women and a child, were reportedly hurt in the strikes.
In an article in an Israeli newspaper, Mr Obama calls the situation a “dangerous moment”.
He is lamenting both the murder of three Israeli teenagers and the killing of a Palestinian boy in what many suspect was revenge.
The president praises Palestinian President Mahmoud Abbas as committed to peace and security co-operation.
The president says the US is still committed to peace despite the recent collapse of US-backed talks.
Overnight, militants in the Gaza Strip unleashed dozens of rockets on southern Israel, setting off air raid sirens and forcing hundreds of thousands of Israelis to stay indoors.
The military rushed more forces to the border and warned that even heavier fighting looked likely.
The latest violence came as Israel pressed forward with its investigation of six Jewish youths suspected of abducting and killing a Palestinian teenager.
Israeli leaders sought to calm an emotional debate over whether the country’s politically charged atmosphere led to the gruesome crime. An Israeli official said three of the youths had confessed to the attack.
Tensions have been high since three Israeli teenagers kidnapped on June 12 in the West Bank were later found dead, followed by last week’s killing of the Palestinian youth in what many suspect was a revenge attack.
Throughout the unrest, Gaza militants have launched more than 200 rockets and mortars into Israel, including close to 100 yesterday alone.
Israel has responded with dozens of airstrikes, but has not been able to halt the attacks. Eight Palestinian militants were killed in fighting yesterday, the highest death toll yet.
Dozens of rockets were fired yesterday, including 40 launched in a single hour after nightfall, setting off air raid sirens up to 50 miles from Gaza, the military said.
Twelve rockets were intercepted by rocket-defence batteries, it added, while the others landed in open areas. It was the deepest penetration of rocket strikes in the current round of fighting and raised the likelihood of an even tougher Israeli response.
Major General Yoav Mordechai, a senior military official, gave a special interview in Arabic to Al-Jazeera, warning that Hamas would bear the consequences for the escalation.
Among the dead were six Hamas militants who Israel said were killed in an accidental blast in a tunnel packed with explosives.
Hamas, the Islamic militant group that controls Gaza, vowed revenge, saying “the enemy will pay a tremendous price”.
Lieutenant Colonel Peter Lerner, an Israel defence forces (IDF) spokesman, said the army was moving two infantry forces to the Gaza border and had received authorisation to mobilise up to 1,500 reservists.
The deaths of the Hamas militants had made a “substantial influence” on the situation, he said.
“There is a potential of deterioration due to their death. Therefore the IDF has to continue to reinforce capabilities in the south, with the potential that things could escalate further,” he said.
In Washington, State Department spokeswoman Jen Psaki said the US condemns the rocket fire. “We also support Israel’s right to defend itself against these attacks,” she said.
Israel has launched two broad military operations in Gaza in the past five years, most recently in 2012, when eight days of heavy fighting ended in an Egyptian-mediated truce.
The increased rocket fire followed the killing of Mohammed Abu Khdeir, a 16-year-old Palestinian boy from east Jerusalem who was abducted and burned to death last week.
Israeli officials on Sunday announced the arrests of six Jewish youths over the killings – ruling out earlier theories that criminal activity or personal reasons might have been a factor.
They said the suspects, including some minors, were from the Jerusalem area.
The teenager’s death triggered several days of violent protests in Arab areas of Jerusalem and northern Israel as Palestinians accused Israeli extremists of killing the boy to avenge the earlier deaths of the Israeli youngsters.
An Israeli official said three of the youths had confessed to the crime and even re-enacted it for authorities.
The official said the suspects included two brothers, and that one of the suspects is the son of a rabbi.
Israel’s Channel 10 TV said the suspects were the son and five grandsons of a prominent rabbi in Jerusalem, without further identifying him. It said two suspects used the rabbi’s car for the kidnapping without his knowledge.
The news that the suspects were Jewish set off nationwide soul-searching over how Israelis could carry out such a gruesome crime. A preliminary post-mortem found that Mohammed was still alive when he was set on fire.
“I am ashamed on behalf of my nation and grieve with you,” President Shimon Peres told the boy’s father, Hussein, in a phone call.
“The only thing left for all of us to do is to ensure that no more children are murdered, and no more tears are shed by mothers.”
Rachelle Fraenkel, the mother of one of the dead Israeli teenagers, said that even from the “abyss” of her own pain, she could not describe her distress over the killing of the Arab boy.
“No mother and father should endure what we are going through now. We feel the pain of Mohammed Abu Khdeir’s parents,” she said.
Also yesterday, Israeli police said a border policeman had been temporarily suspended from special operations and transferred to a different position until the completion of an investigation into the apparent police beating of Tariq Abu Khdeir, a Palestinian-American teenage cousin of the murdered Palestinian youth.