Abu Mazen is another name for Abbas, whose government now includes Hamas, which controls Gaza.
Abbas called an emergency meeting of his own. The Palestinian leadership is expected to meet Tuesday to discuss the developments.
U.S. President Barack Obama, Pope Francis and U.N. Secretary-General Ban Ki-moon were among world leaders condemning the killings Monday.
"As a father, I cannot imagine the indescribable pain that the parents of these teenage boys are experiencing. The United States condemns in the strongest possible terms this senseless act of terror against innocent youth," Obama said in a statement.
He continued: "From the outset, I have offered our full support to Israel and the Palestinian Authority to find the perpetrators of this crime and bring them to justice, and I encourage Israel and the Palestinian Authority to continue working together in that effort. I also urge all parties to refrain from steps that could further destabilize the situation."
Last week, the Israel Security Agency said it believed that two "Hamas activists from Hebron" were behind the teens' disappearances. It identified them as Marwan Qawasmeh, 29, and Amar Abu-Isa, 32.
As Israeli media were reporting on the bodies' discovery Monday night, Israeli forces were blocking roads into Hebron, a city in the southern West Bank. Fighter jets could be heard flying low over Gaza.
Overnight into Tuesday, more than 40 Israeli airstrikes hit Gaza, according to Palestinian security and medical sources. The strikes targeted Hamas, Islamic Jihad and other militant groups, the sources said.
The Israeli military later said that forces had carried out strikes against 34 targets in Gaza, targeting terror infrastructure, after the firing of 18 rockets at Israel since Sunday evening.
Within days after the teens disappeared, Israeli security forces conducted an extensive search for them and detained more than 150 Palestinian suspects.
Netanyahu blamed Hamas for the kidnappings almost immediately. A Hamas spokesman said in the days after the abductions that the Prime Minister's comments attributing blame were "stupid and baseless."
Also in the days after the abductions, the mother of one of the teenagers spoke to reporters.
The three "were just on their way home," said Naftali's mother, Racheli Frankel. "We trust" that they "will be with us here, and we'll hug them soon."