Mr ElBaradei said the elections risked bringing chaos and instability, and possibly military intervention.
The decision to take on the Mubarak regime had not initially been part of his plan, ElBaradei said.
"Whatever our differences are, they should be solved peacefully, " Mr ElBaradei said in a press conference after the al-Azhar meeting on Thursday.
Mr ElBaradei said it was "very important for the IAEA to come to a conclusion that the Iran programme is for peaceful purposes".
Mr ElBaradei said the basic problem was that Mr Morsi's Muslim Brotherhood had spent 80 years in opposition, and was now "intoxicated with power".
Mr ElBaradei said the deal was a chance to "reverse course".
Mr ElBaradei said he would like Israel, along with other Middle East countries, to open up nuclear facilities to inspections by the UN's International Atomic Energy Agency.
Addressing IAEA governors in Vienna on Thursday, Mr ElBaradei said his inspectors had made no progress in their attempts to verify the peaceful nature of Iran's nuclear programme.
The Constitution Party came too late to field a candidate in the 2012 presidential election, but Mr ElBaradei said the aim was to take power in 2016, with Egyptians united behind democracy.
And while intelligence reports suggests Iran is five to 10 years away from a bomb, a year or two of sanctions in counter-retaliations, ElBaradei said, would make terrorism and militancy worse across the Middle East.
"In less than a year in office, he has transformed the way we look at ourselves and the world we live in and rekindled hope for a world at peace with itself, " Mr. ElBaradei said in a statement.
However the head of the IAEA, Mohamed ElBaradei has said that Iran does have a proposal of its own.
"We still have work to do, " the head of the International Atomic Energy Agency, Mohamed ElBaradei, said in Dubai.
Mr. ElBaradei has said he won't run for president unless Mr. Mubarak makes key changes to the constitution, including lifting barriers for independent candidates.
But Mr ElBaradei has said the "jury is still out" on whether Tehran is secretly developing nuclear weapons, because he has no clear proof.
"I could not think of anybody who is more deserving, " said ElBaradei, the chief of the International Atomic Energy Agency.
Several prominent opposition leaders, including Nobel Peace Prize laureate Mohamed ElBaradei, have said they will not engage in dialogue until the president rescinds the measure, known as the constitutional declaration.
It said Mr ElBaradei hoped that Tehran's response "will equally be positive, since approval of this agreement will signal a new era of co-operation".
Members of the Bush administration scorned the Egyptian diplomat, believing he had actively sought to undermine U.S. attempts to pressure Iran over its nuclear program while heading the IAEA. They specifically said Mr. ElBaradei buried documents that showed Tehran had been experimenting with building nuclear warheads and long-range nuclear-tipped missiles.
In April 2012, Mr ElBaradei launched a new political party which he said would be above ideology.
He met with opposition leaders on Saturday, but state news said opposition leaders Hamdeen Sabahy and Mohamed Elbaradei decided not to meet with Kerry.
CNN: Police station torched as fighting engulfs Egyptian city
He said the NSF had unanimously decided to endorse Mr ElBaradei's call.
Iran ultimately balked, but Mr. Elbaradei coordinated closely with Mr. Obama in developing the project, said U.S. officials, and the Egyptian traveled to Tehran to try and cinch the deal.
"Today was important to see who is with us still after the president's speech, and I think we have our answer, " said Basem Kamel, an organizer in opposition leader Mohamed ElBaradei's youth movement, which has been a driving force in organizing and sustaining the demonstrations.
Among the signs that the regime and opposition alike were starting to look toward a post-Mubarak Egypt, Mr. ElBaradei, the Nobel Peace laureate and former head of the International Atomic Energy Agency, said opposition leaders have begun working on a provisional constitution, without specifying who had been invited to draft the document.
"I support ElBaradei, my father wants (Arab League Secretary General) Amr Musa, " one man said.
Mohamed ElBaradei, who won the 2005 Peace Prize for his efforts to prevent nuclear energy being used for military means, said Obama deserved to win for his efforts to bring Iran to the table for direct nuclear talks with the United States.
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