Fatah leader Abbas said he does not agree with Meshaal, who said Hamas will never recognize Israel during his visit to Gaza.
"We recognized Israel in 1993," Abbas said during a visit to Ankara, Turkey. "There is an agreement between Fatah and Hamas that recognizes the two-state solution. Meshaal approved this agreement."
Israeli Prime Minister Binyamin Netanyahu criticized Abbas for not condemning Meshaal's comments outright, Haaretz reported.
The Palestinians "have absolutely no intention of compromising with us," Netanyahu said. "They want to destroy the state. They will of course fail ... The nation of Israel will overcome these hostile enemies."
The controversy comes amid unification negotiations between the rival Palestinian parties Fatah and Hamas.
Abbas said now that 138 countries have voted for Palestine's non-member observer status with the United Nations, it's time to focus on the goal of unity.
"Our first step in this regard is to reach reconciliation. We have taken these steps with Hamas and Egypt," he said, referencing talks set to take place in two weeks in Cairo, Turkey's Hurriyet Daily News reported.