"An al-Sisi presidential bid would come in response to a popular demand," the group said in a statement following a Friday meeting of its political bureau.
Al-Sisi, widely seen as the driving force behind Morsi's ouster, has remained tight-lipped as to whether he plans to vie for Egypt's top office. But speculation has been rife that he would soon resign from his military post to make way for a possible presidential bid.
"As he responded to the demands of the people who took to the streets against the Muslim Brotherhood on June 30, al-Sisi is surely obliged to run for the presidency in response to the people's demand," the group asserted.
It also called on the army chief to adopt "an electoral platform that reflects the January 25 and the June 30 revolutions," referring to the 2011 uprising that toppled Hosni Mubarak and the mass protests that culminated in Morsi's ouster last summer.
On Wednesday, Kuwaiti newspaper Assiyasa quoted al-Sisi as saying that he had decided to run in upcoming presidential polls.
"Yes, it's final. I have no choice but to answer the call of the Egyptian people," the paper quoted al-Sisi as telling its editor-in-chief.
"I cannot turn down the people's request. I will seek their confidence through the ballot box," he reportedly added, according to the interview published on the newspaper's website.
Only hours later, however, army spokesman Ahmed Mohamed Ali dismissed what was said in the interview as "mere speculation."
"Running for president is a personal decision that Field Marshal al-Sisi will decide upon and announce to the Egyptian people in a clear, direct manner," Ali asserted.
Last month, Egypt's Supreme Council of the Armed Forces (SCAF) voiced its "respect" for "popular demands" for al-Sisi to contest presidential polls.
It described the people's "confidence" in al-Sisi as "a call that should be answered."
Interim President Adly Mansour recently issued a presidential decree promoting al-Sisi to field marshal, the highest rank in Egypt's military hierarchy.
The promotion came amid widespread speculation that al-Sisi plans to step down as defense minister to make way for a presidential run.
According to an earlier decision by Mansour, presidential elections will be held less than three months before Egypt's parliamentary polls.
A transitional roadmap, imposed by the army in the immediate wake of Morsi's ouster, had initially called for parliamentary polls to precede presidential elections, following the endorsement of a new constitution.
Born in 1954, al-Sisi graduated from Egypt's Military College in 1997. He served as a paratrooper in the army before being promoted to commander of Egypt's Northern Military Zone.
Al-Sisi had also served as Military Intelligence chief during Egypt's January 25 uprising, which unseated autocratic president Hosni Mubarak in early 2011.
He currently heads up the SCAF, which ran the country's affairs from Mubarak's departure until Morsi became the country's first freely elected president in mid-2012.
Shortly after taking office, Morsi appointed al-Sisi as defense minister.
One year later, however, the army chief removed Morsi from office – and later had him detained on criminal charges – following mass protests against his presidency.