ISTANBUL — After prayers on Friday, Prime Minister Recep Tayyip Erdogan stepped outside a mosque on the banks of the Bosporus here and dismissed a suggestion that Turkey should talk directly with a onetime ally, Israel, to attempt to resolve the crisis unfolding in Gaza.

“We do not have any connections in terms of dialogue with Israel,” he said.

But by Tuesday, Turkey seemed to indicate that while its strident anti-Israel posture has been popular among Arabs, it has been at its own expense, undermining its ability to play the role of regional power broker by leaving it with little leverage to intercede in the Gaza conflict. As he headed to Gaza with an Arab League delegation on Tuesday, Turkey’s foreign minister, Ahmet Davutoglu, suggested to reporters that back-channel discussions had been opened with Israeli authorities.

“Turkey’s new foreign policy has but one premise, to become a regional actor,” said Soner Cagaptay, a Turkey expert at the Washington Institute for Near East Policy. “To this end, Ankara needs to have persuasive power on all countries of the region. In the past decade, Ankara has won that power with the Arabs but lost it with the Israelis.”