Egypt's ambassador to the U.S. says the Muslim Brotherhood should "join the process" and accept deposed president Mohamed Morsi's ouster.

"My advice to the Muslim Brotherhood is they need to acknowledge the mistakes that they made and they need to join the process. Let us look ahead to the future," Egyptian Ambassador Mohamed Tawfik told ABC News Chief White House Correspondent Jonathan Karl on "This Week" Sunday. "There is room for everyone in Egypt, but there is no room for violence, there is no room for incitement to hatred and incitement to commit acts of violence."

A member of the Muslim Brotherhood political party in Egypt, Morsi was democratically elected last June only to see a swell of popular opposition one year later. Last week, the Egyptian military removed Morsi from power and installed an interim president, Adly Mansour.

Tawfik was appointed by Morsi to his current post but now supports the movement against Morsi.

The ambassador said on "This Week" that Morsi was deposed because he did not act in the interest of all Egyptians - the same criticism leveled by protesters who say Morsi pursued a religious agenda at the expense of Egypt's economy.

"Morsi was elected democratically, I agree. I supported him. I did my best to help him to succeed," Tawfik said. "President Morsi did not act in the interests of the vast majority of Egyptians. He only looked at his own clique. You can't be a democratically elected president and act that way. So now, we want new elections. We're going to get new elections. We're going to get a new parliament."

Those elections will happen "as quickly as we can put it together," Tawfik said.

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Meanwhile, $1.5 billion in U.S. aid hangs in the balance, as U.S. law prohibits aid from being sent to countries where democratically elected leaders are overthrown in military coups.

On that key issue, Tawfik and the Muslim Brotherhood now disagree on whether Morsi's ouster qualifies as a coup.

"Egypt has not undergone a military coup and it is certainly not run by the military," Tawfik said on "This Week." "What happened was you had over 15 million people in the streets. And President Morsi, he could have said, 'Listen, my people, I listen, I hear you.' But instead of that, he whipped up religious fervor among his supporters, and there was violence in the air."

The Muslim Brotherhood sees it differently.

"I don't understand what naivete can behold any person to see all the ingredients, political science wise, of a coup, and not see the coup," Muslim Brotherhood spokesperson Gehad el-Haddad told ABC News' Byron Pitts in Cairo. "It's military junta on TV, tanks on the streets, troops on protest. Military people shooting civilians. I mean, it's every ingredient of a full police state. I mean, what else are people waiting for?"

El-Haddad said the Muslim Brotherhood has no backup plan if the military will not return Morsi to power. He said he is willing to die protesting Morsi's removal.

"There is no plan B," el-Haddad said. "We will stick by our principles. We either return the president back to his rightful place, or they are just going to have to shoot us in the street."

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