Tantawi, an ex-defence minister and confidante of the ousted leader, said he is too busy dealing with security issues arising out an attack on Israeli embassy, to testify at Mubarak's trial, the BBC reported.
The court had asked him as well as chief of staff Sami Anan to testify whether the army received orders to open fire on the protesters in particular on the night of January 28 after the police withdrew from the streets and the army was deployed to keep order.
The court postponed his appearance until September 24 and 25.
Mubarak is charged with ordering the killing of protesters during the uprising that toppled him in February. Nearly 900 people died in the unrest.
The trial comes amid a diplomatic row between Israel and Egypt following the vandalisation of the embassy of the Jewish nation. Ambassador Yitzhak Levanon, members of the diplomatic staff, their family members and other Israelis had to sneak out of Cairo in a special Israel Air Force carrier.
In another trial of senior officials of the former regime for what is known as the 'battle of the camel' started here.
In this case scores of figures from the former regime are accused of arranging an attack on the protesters who were staging a sit-in in Cairo's Tahrir square on February 2, 2011 killing many, injuring scores others as well as inflicting disabilities on many others.
The protestors in the square were attacked by men on horse and camel backs carrying whips, knives and molotov cocktails.
Among the most prominent accused are the former speakers of both houses of parliament as well as leading figures of the former ruling party.
The former speaker of the higher house of parliament Safwat al-Sharif was also the general-secretary of the former ruling party.
Al-Sharif was considered the mastermind behind Egyptian politics for decades as he was a pillar of the Egyptian intelligence before.
This is the first time Al-Sharif appears in a dock after having been arrested months ago.
This court session is being relayed live on Egyptians television as the requests of the revolutionaries.
The prosecution read out the accusations which the accused vehemently denied.
The first few sessions in such cases are generally procedural.