All that said, the highlight of the conversation dealt with the 2009 raid. Israel has long stood by the operation, though its tune publicly changed Friday.
"In light of Israel's investigation into the incident, which pointed out several operational mistakes, Prime Minister Netanyahu expressed Israel's apology to the Turkish people for any mistakes that might have led to loss of life or injury and agreed to conclude an agreement on compensation/nonliability," the Israeli government said.
Asked to confirm whether Netanyahu called and apologized and offered compensation, as Ankara had long demanded, a senior Turkish official told CNN: "Yes." Erdogan only said they "agreed to conclude an agreement on compensation/nonliability."
One Palestinian-Israeli lawmaker doesn't like it
Hanin Zoabi, a Palestinian activist who was on the Mavi Marmara and also is a Palestinian member of Israel's parliament, said she does not accept Netanyahu's apology. She wants an international court to try the people "involved in the political decision that gave a green light to kill the political activists on the Marmara."
She said Netanyahu's push to improve Israeli-Turkish ties is undermining the Palestinians' demands -- such as ending Israeli occupation of the West Bank and the Israeli military and economic strictures on Gaza. She said Netanyahu is trying to evade that and other issues.
"The issue is not only Marmara, Marmara was the small crime. The big crime was the siege on Gaza," she told CNN.
Gulden Sonme -- a spokeswoman for IHH, the Muslim aid agency that operated the Mavi Marmara == called the apology "a positive political development."
"But in terms of the need for the blockade on Gaza to end and in terms of the ongoing case to punish those who are responsible for the crimes committed during the raid, the legal process will continue," she said, referring to the case against the soldiers.
Suat Kiniklioglu, a Turkish political analyst and former parliamentarian from Erdogan's party, said the apology is important because it shows "to the world that there is a political price to kill Turkish citizens in international waters."
"Probably in the Middle East, as well, it will be seen as political victory for the Erdogan government. But what matters more is the normalization itself, the obvious benefits to Turkey and Israel as well as the Palestinians."
The prospect of an Israeli-Turkish reconciliation is bad news, Kiniklioglu said, for Syrian President Bashar al-Assad and Iran.
"As Syria is entering into its third year of uprising, Ankara and Tel-Aviv will have to coordinate policy and may need to work together to contain potential risks to both countries," he said.