The talks come just three days after King Mswati III led a failed effort by African leaders to rescue a faltering power-sharing deal in Zimbabwe.
A new summit is set for Monday in Harare, where southern African leaders will try to break an impasse on forming a unity government in Zimbabwe, seen as the best chance for ending the country’s political turmoil and halting its economic decline.
Menkerios also plans to discuss the conflict in the Democratic Republic of Congo and other regional security issues, foreign ministry spokesperson Clifford Mamba said in a statement.
"He will be consulting with the king on the issues of security and peacekeeping in (southern Africa), especially on Zimbabwe and the Democratic Republic of Congo," Mamba said.
The king chairs the security organ of the 15-nation South African Development Community (SADC).
King Mswati had gathered the presidents of South Africa, Mozambique and Congo in Swaziland’s capital on Monday in hopes of ending the deadlock in Zimbabwe.
President Robert Mugabe attended the meeting, but Zimbabwe opposition leader Morgan Tsvangirai refused to attend.
A new summit has been set for October 27 in Harare in hopes of settling differences between the rivals over control of powerful ministries – particularly home affairs, which oversees the police force.
Menkerios on Tuesday voiced confidence that a deal would be reached in Zimbabwe.
"I am confident that a deal will be reached between the two because both sides know by now that there is no other way, but to sit down and reach an agreement," he told AFP in Addis Ababa.
Menkerios was also expected to discuss renewed fighting in the Democratic Republic of Congo, where the UN said on Tuesday that more than 50 000 people fled their homes following intense fighting between government and rebel troops in the northeastern Ituri region.
Fighting in late August in nearby Nord-Kivu province has also displaced another 100 000 people.
More than one million people have been forced to flee their homes in the region, aid agencies say.