Other cries of "down with the military rule" came from the room, while el-Sissi supporters yelled "long live Egypt" as the two leaders left the room.
During the news conference el-Sissi defended the tentative death sentence handed to his predecessor Mohamed Morsi last month. He said Morsi, whom he ousted from power, will have chances to appeal.
Merkel said she had brought up the issues of human rights abuses and the death penalty as areas where the two countries had "differences of opinion."