CAIRO (Reuters) - Egypt's army chief Abdel Fattah al-Sisi said in a speech on Sunday that no movement would be barred from participating in politics, as he sought to explain his decision to oust elected President Mohamed Mursi amid fierce criticism from Islamists.

Addressing an armed forces gathering in Cairo, Sisi said Mursi had lost legitimacy because of mass demonstrations against him.

"Every political force without exception and without exclusion must realize that an opportunity is available for everyone in political life, and no ideological movement is prevented from participating," he said.

Sisi said that in the days running up to Mursi's ouster on July 3, the military had urged the former Islamist president to hold a referendum on his rule.

It was the first official confirmation of details of the days before the dramatic overthrow, first reported by Reuters.

"I sent delegates to the former president...to call for a popular referendum, and the response was total rejection," the army commander said.

Sisi said the military had a duty to maintain "a distance from politics" but that its national responsibility forced it to act against Mursi, who it says did not represent the will of the Egyptian people.

Supporters of Mursi's Muslim Brotherhood are furious at the military intervention, and some foreign governments, including the United States and Germany, have criticized the army's crackdown on the movement.

"The guy is either lying or his troops are operating without his knowledge, because the only thing we're seeing from him are arbitrary arrests, confiscation of assets and killing of our protesters," said Brotherhood spokesman Gehad El-Haddad, in response to Sisi's speech.

On Monday, 53 Mursi supporters were killed at the Republican Guard compound in Cairo when troops opened fire. Four soldiers were also killed in a clash the military says was provoked by an attack and which the Brotherhood calls a "massacre".

In his speech, the army chief said his role was temporary and blessed by some of Egypt's most prominent religious and opposition figures.

"The Egyptian military is preparing to complete its work and is apolitical. It has laid down a future plan which facilitates the right of free choice and this plan was blessed before the Egyptian people through its main representatives," Sisi said.

"I don't want to dwell long on the past, but on the present and on the future, because that is what we are able to choose and we deal with it in a way the people want," he said.

"All the political powers of the people now stand at a crossroads," he said.

(Reporting by Noah Browning and Yasmine Saleh; editing by Mike Collett-White)