African leaders, including Mugabe, are gathered for an African Union summit in the Egyptian Red Sea resort of Sharm el-Sheik, Voice of America reported Monday.
Mugabe arrived at the summit hours after he was sworn in for a sixth term in office.
He won a runoff election Friday in which he was the only candidate and which has been widely condemned.
Opposition candidate Morgan Tsvangirai of the Movement for Democratic Change dropped out of the race amid concerns for his life.
"I would hope that the African Union with the United Nations will make it absolutely clear to Mr. Mugabe that there has got to be change, a new government has got to be brought in and that when democracy is restored in Zimbabwe we will prepared to help the Zimbabwean people end the poverty and the deprivation and the famine that exists in some parts of the country," Brown said.
The European Union called Mugabe's election victory as "an exercise in power-grabbing."
EU Development Commissioner Louis Michel also called for the African Union to seek a political solution.