An alliance of Somali opposition parties has proposed the creation of a national governing council, after the president's term expired on Monday with no clear plan for succession.
The power vacuum and divisions between political leaders was a boost to the Al Qaeda-linked Al Shabaab insurgency, a Somali security analyst warned, citing a spate of recent attacks in a relatively peaceful part of the country.
The opposition alliance said they would reject any attempt to extend the term of president Mohamed Abdullahi Mohamed, and suggested the council could elect a transitional leader to govern until a new president can be chosen by politicians.
"We are against time extension, suppression, violence and further delay to the election," the alliance said in a statement.
"An election schedule should immediately without delay be displayed with agreed upon specified time."
There was no immediate comment from the presidency, although aides had previously privately floated the idea of extending Mr Mohamed's term.
Somalia was initially planning to hold its first direct election since civil war erupted in 1991, but delays in preparations and continuous attacks by Al Shabaab forced the country to plan another indirect vote.
Instead of a one-person-one-vote election, senators and members of parliament are elected by community leaders such as delegates of powerful clans in each state.
Clan elders should have cast their votes in December, and parliament was set to choose a new president on Monday.
However, the election was delayed after the opposition accused Mr Mohamed — who was seeking a second term — of packing regional and national electoral boards with his allies.
President blames 'foreign interventions'
Leaders in two of Somalia's five federal states, Puntland and Jubbaland, said they would no longer recognise Mr Mohamed.
In turn, he accused them of reneging on a September agreement that meant the president could stay in office after the election date if needed.
United Nations observer James Swan said any delay brought "an unpredictable political situation in a country where we certainly don't need any more of that."
The president was booed in parliament on Saturday after he blamed "foreign interventions" for disrupting the election process.
The Jubbaland leader, Ahmed Madobe, said the president "spoke to me in a disgusting way … He keeps accusing us of being supported and manipulated by Kenya."
Late last year Somalia broke off diplomatic relations with Kenya, accusing it of meddling. Kenya has denied it.
Mr Madobe also objected to the recent deployment of federal troops to a border community in his region next to Kenya, calling it an attempt to undermine his authority.
"I tried everything I could to solve this crisis in the best logical way together with the rest of the federal member states, but it was always the president who refused," Mr Madobe said.
Hussein Sheikh Ali, Somalia's former national security advisor and founder of the Mogadishu-based Hiraal think tank, said Al Shabaab had already taken advantage of the security vacuum to launch attacks in portions of central Somalia that had been relatively peaceful for around a decade.
"They [Al Shabaab] are laughing out loud," he said.
"This is a failure by the president, Somalia's political elite and the international community. They didn't have a plan B to move forward."
Somalia election delay leads to fears Al Shabaab could exploit power vacuum
Somalia's opposition stops recognising president Mohamed Abdullahi Mohamed as elections are delayed and analysts fear the Al Qaeda-linked Al Shabaab could exploit the power vacuum in the country.
