"No cause for alarm, the South African government remains," and will continue to focus on the issue, Kikwete, who is president of Tanzania, told the U.N. General Assembly.
The African Union "stands ready to assist, if need would arise," he told the 192 U.N. member states.
Mbeki, who accepted a demand from his own party to resign on Monday, helped mediate the agreement between Zimbabwean President Robert Mugabe and opposition leader Morgan Tsvangirai, but there is deadlock over Cabinet posts.
Tsvangirai’s Movement for Democratic Change has said it does not oppose Mugabe taking charge of the army, but he has also insisted on keeping control of all key ministries, including those that oversee the police, foreign affairs, finance, justice, information and local government.
U.S. Assistant Secretary of State for African Affairs Jendayi Frazer told Reuters on the sidelines of the U.N. meeting that Washington was concerned with the deadlock over the Cabinet posts in Zimbabwe and has a new batch of sanctions ready if Mugabe reneges on his promises.
Despite the impasse, Kikwete said "getting to this point in a conflict situation that looked impossible to resolve is a major achievement."
"This is testimony to the fact that democracy and good governance are taking root, and the African peace and security architecture is working," Kikwete said.
Still, he said more could be done to strengthen the African Union’s capacity for conflict prevention and resolution.
Addressing the conflict in Sudan’s Darfur region, Kikwete said that situation could be improved with a planned full deployment of 26,000 U.N.-African peacekeepers, and if humanitarian work was allowed to be carried out unimpeded.
He said the volatile security situation in eastern Democratic Republic of Congo was of "great concern" and the African Union was committed to be more proactive in helping to end the fighting between government and rebel forces.
He called on the United Nations to take over peacekeeping from an overstretched African force in Somalia, where rebels have waged an Iraq-style insurgency of mortar attacks and roadside bombings against a fragile Western-backed interim government.