Mr. Mugabe spoke at the funeral of Vice President Joseph Msika, 85, who served alongside Mr. Mugabe for two decades and died last week after suffering from heart disease for many years.
Prime Minister Morgan Tsvangirai and other top officials in the five-month-old coalition government joined Mr. Mugabe and 20,000 other mourners at the Heroes Acre cemetery in Harare, the capital. Mr. Mugabe was the only one to speak.
Mr. Mugabe often turns his addresses at state funerals into fiery political speeches. His speech on Monday came after Secretary of State Hillary Rodham Clinton visited neighboring South Africa last week and called on its government to help Zimbabwe cope with what she called the “negative effects” of Mr. Mugabe’s leadership.
Mr. Mugabe did not mention Mrs. Clinton by name but said his coalition with Mr. Tsvangirai, formerly the leader of the opposition, was working and was supported by southern Africans.
“Who is the real judge of the political arrangement that we have done here in southern Africa?” Mr. Mugabe said. “Why should America not recognize the work we are doing as an inclusive government? These Anglo-Saxon nations are giving us problems. We tell them today, ‘Leave us alone. We don’t need your interference because we can do it alone.’ ”
His many critics say Mr. Mugabe has brought a prosperous nation to ruin during decades of authoritarian rule.
A former South African president, Thabo Mbeki, brokered Zimbabwe’s coalition agreement after Mr. Tsvangirai finished ahead of Mr. Mugabe in the first round of presidential polling last year, but pulled out of a runoff because of state-sponsored violence against opposition supporters.
Since joining the coalition, Mr. Tsvangirai has accused hard-line supporters of Mr. Mugabe of stalling political reforms and continuing to harass his supporters.