Mubarak feels "humiliated and embittered at Obama's most recent statement about the need for him to resign immediately", so he rejected the call.
The report adds that the former president is residing at his palace in Sharm el-Sheikh and maintaining a similar lifestyle, though he has hired additional guards.
Israel has also approved the entry of two Egyptian army battalions into the southernmost Sinai city in order to help guard the palace.
Mubarak's health is deteriorating rapidly, the report says, and has been since he was forced to leave his Cairo residence. Saudi King Abdullah has offered him asylum in his country, but the former leader refused, saying he would like to die on Egyptian land.
In addition, Mubarak continues to employ the aides who worked under him during his term as president, the report says, adding that the military has apparently "decided to grant Mubarak an honorable resignation" as no one has threatened him with charges of unlawful activity, though other officials have been accused of corruption.
