"I appreciate what president Abbas said a few days ago in Saudi Arabia, rejecting the kidnapping," Netanyahu told his Romanian counterpart Victor Ponta at a meeting in Jerusalem.
"I think these were important words," he said, according to a statement.
The three Israeli teenagers disappeared from a hitchhiking stop in the southern West Bank on June 12, with Israel rounding up hundreds of Palestinians as part of an operation to find them while also dealing a crushing blow to Hamas's West Bank network.
Israel has accused Hamas of kidnapping the youngsters, but the Islamist movement has not claimed their abduction.
Abbas also pledged to continue security coordination with Israel, which he said was in Palestinians' "best interest" since it would "help protect us".
Israel has seized on the opportunity presented by the operation to try to rupture a reconciliation agreement between Abbas and Hamas, which saw the two sides recently agree on an interim unity government of independents.
Netanyahu slammed Meshaal's remarks, reiterating that if "Abbas really means what he said about the kidnapping, and if he is truly committed to peace and to fighting terrorism, then logic and common sense mandate that he break his pact with Hamas."
"There can be no alliance with the kidnappers of children," he said.
Israel has since the beginning of its operation arrested 354 Palestinians throughout the West Bank, 269 of them Hamas activists, the army says.
Today, army radio reported the Israeli cabinet had decided to scale down the arrest campaign and focus on searching for the teens.
