Somali Prime Minister Ali Mohammed Ghedi has been called to Ethiopia's capital to meet the prime minister.
Mr Yusuf (l) and his prime minister (r) no longer see eye to eye
Mr Ghedi is embroiled in a quarrel with the president of the Somali transitional government and was facing a vote of confidence in parliament.
The vote has now been postponed until after his return.
Ethiopian troops intervened to save Somalia from being overrun by Islamist militias at the end of last year.
The BBC's Elizabeth Blunt in the Ethiopian capital Addis Ababa says that Ethiopia's intervention in support of Somalia's transitional federal government has cost it money and the lives of some of its soldiers.
But, she adds, it has also cost it the goodwill of some of its own Somali-speaking citizens in the south-east of the country, where the sight of Ethiopian troops fighting fellow Somalis has stirred up old animosities and added fuel to a long-smouldering rebellion.
She says the whole carefully pieced-together structure in Somalia is teetering, not because of Islamist attacks but because of a quarrel between the two leading players Mr Ghedi and President Abdullahi Yusuf.
With each of them going around protected by militia from their own clans, the quarrel could easily spill over into open violence.
Ethiopia first sent its minister of tourism to Somalia to urge them to agree - not at first sight an obvious choice but he is the most senior Somali speaker in the Ethiopian government.
Then on Wednesday it summoned Mr Ghedi to Addis Ababa.
He went vowing that he intended to remain as prime minister but with rumours swirling round Somalia that he might not return.