Mr Yusuf (left) has been criticised by African leaders for appointing Mr Guled
A spokesman for Somali President Abdullahi Yusuf Ahmed has denied media reports he plans to resign on Saturday.
Spokesman Walak Salih told the al-Jazeera TV network that the reports, which quoted Mr Yusuf's political allies, were "baseless rumours".
Earlier, the man appointed prime minister last week by the president announced his resignation.
Mohamed Mahamud Guled said he was stepping down because his appointment was destabilising the government.
Mr Guled said he had made the decision "so that I am not seen as a stumbling block to the peace process which is going well now".
He was appointed in defiance of Somali MPs, who said the dismissal of his predecessor, Nur Hassan Hussein, two weeks ago, had been illegal.
The president had clashed in recent months with Mr Nur over attempts to negotiate a peace deal with the Islamist-led armed opposition.
Earlier this week, East African leaders imposed sanctions on Mr Yusuf.
At a meeting in Addis Ababa, the Inter-governmental Authority on Development (Igad) said it would not recognise the unconstitutional appointment of Mr Guled, and gave its backing to Mr Nur.
The grouping also called on other countries to take similar measures.
The BBC's East Africa correspondent Karen Allen says it is a sign of just how exasperated the international community has become with a country which has been in the grips of a power struggle for the past 17 years.
Splits have paralysed Mr Yusuf's Western-backed administration at a time when Islamist insurgents appear to be growing stronger by the day.
Earlier, speaking to reporters in the town of Baidoa, Mr Guled said that "after evaluating the current situation", he had decided to resign as prime minister.
"I stood down so that I am not seen as a stumbling block to the peace process which is going on well now," he added.
"I want the government to remain in power and differences among its leaders to be sorted out."
Mr Guled, the former interior minister, said he hoped the president would accept his decision, and that he would remain a member of parliament.
When Mr Yusuf sacked Mr Nur, he said it was because his government had been "paralysed by corruption, inefficiency and treason" and had failed to bring peace.
Nur Hassan Hussein said the president did not have the power to sack him
However, Somalia's parliament declared the sacking illegal and passed a vote of confidence in Mr Nur by a huge majority the following day.
Somalia has not had a functioning national government since President Mohamed Siad Barre was overthrown in 1991.
Ethiopian troops intervened two years ago to oust Islamists from Mogadishu, and install the transitional government.
But it is now in disarray and only controls parts of the capital and the town of Baidoa after recent advances by different Islamist groups.
On Monday, the African Union agreed to keep its small peacekeeping force in place for a further two months, but did not say how it would cover for the imminent Ethiopian withdrawal.