(CNN) -- Israel's decision in May to intercept an aid flotilla headed to Gaza -- an incident that left nine people dead -- remains a diplomatic stumbling block between Israel and Turkey, the countries' leaders said Sunday.
Israeli President Shimon Peres and Turkish President Abdullah Gul both appeared, separately, on CNN's "Fareed Zakaria GPS," where they gave their points of view on the contentious issue that has divided the traditional allies.
The flotilla, which carried thousands of tons of humanitarian aid, departed from Turkey to Gaza, and eight Turks were among those killed. The other victim had dual Turkish-U.S. citizenship.
Israel says that Turkey has frozen relations because it refuses to apologize for the storming of the flotilla, which was seeking to break an Israeli blockade to Gaza.
"We were friends of Turkey. We shall seek friendship with Turkey. Maybe Turkey has changed their policies. It's her consideration," Peres said.
He added, "We don't think that we did anything wrong on the ship."
The United Nations' Human Rights Council concluded last week that Israeli forces committed serious violations of international law in the incident.
"The fact-finding mission concluded that a series of violations of international law, including international humanitarian and human rights law, were committed by the Israeli forces," said the 56-page report released by the commission.
The Israeli government dismissed the report as "biased" and "one-sided."
Israel has maintained its troops used force on the activists only after they were attacked by those on board one boat. Soldiers were attacked with knives, metal poles and other objects, Israeli officials have said.
But passengers on board the boat insist Israeli troops fired on them without provocation.
Gul said that Turkey is not demanding an apology, but is expecting Israel to recognize its culpability in what international organizations have criticized as a disproportionate response to the flotilla.
"They are defending their act and they are criticizing us as if we acted something wrong. With this understanding how can I meet?" Gul said.
Peres described a meeting that was supposed to take place between himself and Gul, but was allegedly canceled because Israel did not apologize or offer compensation to Turkey.
Gul said that that version is "not correct."
"This is not our choice, you see," Gul said. "We do not prefer this deterioration in relationship but unfortunately it was a great mistake from Israeli side because this blockage, embargo on Gaza."
Turkey wants to see the embargo lifted.
Peres defended the decision to intercept the flotilla, saying that the Israeli military communicated with the ships and told them that if they wanted to deliver aid, they could go a port in Israel or Egypt and it would be transported to Gaza.
"No, they wanted a provocation. What for?" Peres asked.
He continued, "I'd say, look, we are friends. We have to continue our friendship. If you want to help in Gaza, start with the reason, not with the reaction. Tell Hamas to stop shooting."
Gul said that after Hamas won elections in Gaza, a delegation from the Palestinian militant group visited Turkey.
"They came. And, we talked with them, all in detail, and we told them, "Look, now, your direction should be different from now. You are elected democratically, you should act democratically. Terror sending is nonsense, rockets -- you stop all these things."
The Turkish president said it was up to Israel to decide if it wanted to re-establish the friendliness that existed before.
In the interview, Peres also touched on the threat he sees posed by Iran and its president, Mahmoud Ahmadinejad.
"I don't believe any word that he says, but I watch everything he does from hanging homosexuals because they are homosexuals, for shooting at the crowd of people who are protesting with fire, for sending arms to Hamas and Hezbollah, for financing terror," Peres said.
Iran seeks to become the most dominant country the Middle East, the Israeli president said.
"Today the choice for the Middle East -- to remain a Middle East of independent countries or to fall under this spell of Iran. They are very ambitious."