CAIRO, June 26 (Reuters) - Egyptian President Hosni Mubarak predicted on Tuesday that the two main Palestinian factions -- Fatah and Hamas -- would soon patch up their differences through dialogue and said that Egypt was willing to mediate. In an interview with Egyptian state television, Mubarak said repeatedly that the two sides needed a period of calm to come to their senses and resume dialogue.

"I believe that after a period of calm, especially as they had a legislative assembly where they (Hamas) had a majority, an understanding between them is bound to come about," he said.

Asked how long the period of calm should be, he said: "Maybe two weeks, maybe three weeks, maybe one month, until people start to think logically and soundly. In that case they are bound to start a dialogue."

Mubarak's approach was a sharp break with recent Egyptian statements on the fighting in Gaza this month, which ended when Hamas took full control and disarmed Fatah forces there.

Mubarak had called Hamas's action a coup and his government has said that it recognises only Palestinian President Mahmoud Abbas of Fatah as the legitimate Palestinian leader.

But on Tuesday Mubarak said that even if Hamas started the trouble in Gaza, the fighting quickly got out of hand and the Palestinian government made "a big mistake" in losing control.

In a speech to Israeli, Palestinian and Jordanian leaders in the Red Sea resort of Sharm el-Sheikh on Monday, Mubarak called for immediate dialogue between Palestinians but he did not make clear whether he was talking about Fatah and Hamas.

Asked whether Abbas had backed away from his refusal to have dialogue with Hamas, Mubarak said that Abbas was still tense because he thought there had been a plot to assassinate him.

"Of course he will be tense ... and he won't accept any dialogue, but it needs a period of calm and a return to sense and logic and after the process calms down, then it (dialogue) becomes possible," he said.

Mubarak said no external party should intervene between the Palestinian factions in the meantime. "We have been mediating between the two sides but it needs a period of calm (for mediation to resume)," he said.

He noted that the main Palestinian factions recently came to Cairo for talks with Egypt and he did not indicate any review of the Egyptian government's policy of talking to them all.

The Egyptian president said there was no evidence that Syria or Iran played a part in the events in Gaza and that Egypt was in constant contact with Iran despite not having formal relations.

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