Israel has carried out more air strikes on the Gaza Strip, following dozens of rockets fired by the Palestinian Islamist movement, Hamas.
Tension has spiked in recent days over deaths of of three young Israelis and the killing of a Palestinian teenager in an apparent revenge attack.
Rachel Fraenkel, whose son, Naftali, was one of three Israeli teenagers kidnapped and killed last month, has urged against vigilante action.
"No mother or father should ever have to go through what we are going through, and we share the pain of Mohammed's parents," Ms Fraenkel said.
The burnt body of 16-year-old Palestinian Mohammed Abu Khudair was discovered in a Jerusalem forest last week.
Israeli police have apprehended six suspects in the Palestinian teen’s death. Three reportedly have confessed.
"Alongside the pain of this terrible act, we take pride in our country's zeal to investigate, to arrest the criminals and to stop the horror..."
On Tuesday, Israeli Prime Minister Benjamin Natanyahu spoke to the family of the Palestinian youth over the phone.
"I wish to express my shock and the shock of Israel's citizens over the despicable murder of your son," Prime Minister Benjamin Netanyahu told the father, according to a statement.
He also promised that those responsible would be brought to trial and prosecuted to the full extent of the law.
Mr Khudair's death followed the kidnap and murder of three Israeli teens on June 12. Israel has blamed Hamas militants for the deaths
Ms Fraenkel said the legacy of the three Israeli teens "is one of love, of humanity, of national unity, and of integrity. Alongside the pain of this terrible act, we take pride in our country's zeal to investigate, to arrest the criminals and to stop the horror, and we hope that calm will return to the streets of our country," she said.
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