ISTANBUL (Reuters) -- Prime Minister Tayyip Erdogan said on Saturday an Israeli apology for the 2010 deaths of nine Turkish pro-Palestinian activists that was brokered by US President Barack Obama met Turkey's conditions and signaled its growing regional influence.

"We are entering a new period in both Turkey and the region," said Erdogan, who plans to visit the Palestinian territories, including the Gaza Strip, next month.

"We are at the beginning of a process of elevating Turkey to a position so that it will again have a say, initiative and power, as it did in the past."

Israeli Prime Minister Benjamin Netanyahu, in a phone call on Friday, agreed to meet Turkey's three conditions for normalizing relations, Erdogan said.

These were a clear apology, compensation to the victims' families and a relaxation of the blockade against Gaza, Erdogan told a rally broadcast live from the western town of Eskisehir.

Israel bowed to a demand by Ankara to apologize formally for the deaths nearly three years ago aboard the Mavi Marmara, a Turkish vessel carrying humanitarian aid and challenging Israel's naval blockade of the Palestinian-run Gaza Strip.

The men died after Israeli marines stormed the ship.

The incident wrecked diplomatic ties between Turkey and Israel, once strategic partners.

Muslim Turkey expelled Israel's ambassador and froze military cooperation after a UN report into the incident released in September 2011 largely exonerated Israel.

"I expressed that normalizing (relations), which will facilitate regional peace, would depend on these steps," Erdogan told reporters on the train to Eskisehir, CNN Turk said.

Reviving the relationship is seen as a key source of stability as the two countries and their Western allies confront civil war in Syria and the prospects of a nuclear-armed Iran.

Erdogan also told the crowd that Obama, who was in Israel on Friday for talks with Netanyahu, had called him before passing the telephone to the Israeli premier to apologize.

The Turkish leader said Netanyahu had told him restrictions on consumer goods reaching Gaza and the West Bank would also be lifted and pledged to seek Turkish help in improving humanitarian conditions in the Palestinian territories.