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Turkish Prime Minister Recep Tayyip Erdogan accused Israel on Tuesday of being behind the military-backed ouster of Egypt's Islamist president Mohamed Morsi last month.

"What do they say about Egypt: democracy is not the ballot box. Who is behind this? It's Israel," Erdogan, an outspoken critic of the Jewish state, told a meeting of his Islamic-rooted Justice and Development Party (AKP).

"We have the evidence," he said, citing what he said were comments by an Israeli justice minister to a 2011 forum in France in which he allegedly said Morsi's Muslim Brotherhood would not be able to remain in power even if it won elections.

But Erdogan's accusation was furiously rejected by Egypt, which said it had "no basis in fact." The claims also drew criticism from the US, with the White House describing the comments as "offensive and unsubstantiated and wrong."

Morsi was sworn in as Egypt's first democratically elected leader in June 2012 but was overthrown by the military last month with popular backing.

Erdogan's AKP, which had developed friendly ties with Morsi and the Muslim Brotherhood, has described his ousting as a "coup."

Turkey's stance has infuriated Egypt's military-backed interim government which last month voiced "strong resentment" at Erdogan's pro-Morsi comments.

On Tuesday, the office of Egypt's new prime minister Hazem al-Beblawi said Erdogan's latest words "have no basis in fact and are not accepted by any sane or fair person."

It said Erdogan's comments were intended to "target Egyptian national unity" and warned that Cairo's "patience was reaching breaking point."

Turkey has hardened its tone towards Egypt's new rulers after last week's bloody crackdown on Morsi supporters, recalling its ambassador to Cairo, prompting a tit-for-tat move by Egypt.

Daily demonstrations in support of Morsi have since taken place in Turkey and the two countries have cancelled joint naval exercises planned for October.