Shia Houthi fighters in Yemen are pressing President Abd-Rabbu Mansour Hadi to appoint a vice president from their group.
The development comes as the Houthi fighters, after taking over the presidential palace in Sanaa following months of political unrest, demand that Hadi implement a power-sharing deal.
The fighters battled guards at Hadi's home in Sanaa and entered his palace on Tuesday.
Al Jazeera's Omar Alsaleh, reporting from the southern city of Aden on Wednesday, said it was not yet clear if Hadi has approved the demands of the Houthis, but given his current tenuous position, he has "no other options but to meet all the demands".
"All of this is happening after a day of heavy fighting, which left President Hadi even weaker," he said.
Also on Wednesday, Ali Abdullah Saleh, the former president, called for early elections, arguing that early presidential and parliamentary polls would help defuse the current political crisis.
Al Jazeera has obtained leaked telephone conversations suggesting that Yemen's deposed leader is working with Houthi rebels to undermine the government.
Abdel-Malik al-Houthi, leader of the Houthis, has accused Hadi of "failing the Yemeni people" and disrupting the implementation of the Peace and National Partnership Agreement (PNPA), which was approved after the Houthis seized the capital, Sanaa, in September.
In a televised speech just hours after his fighters' display of force on Tuesday, Houthi warned Hadi that he had to implement the power-sharing deal.
"At this historic and exceptional point in time, when conspiracies have been plotted against the country, there is a great danger facing Yemen,” Houthi said.
“Nothing will ever stop us from realising the peace and cooperation treaty. We will not be scared by foreign powers, the issue is crucial."
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The Houthis are demanding security solutions and reforms to the national decision-making body, and they reject the draft constitution that divides Yemen into six federal regions.
Houthi fighters stood guard on Wednesday outside the private residence of Hadi, whose home in the city centre is normally protected by presidential security officers, witnesses said.
Entry posts were empty and there was no sign of the presidential guard at the compound, scene of clashes between Houthis and guards on Tuesday, the witnesses said.
Under house arrest
An official at the president's residence told Al Jazeera that Hadi had not been harmed in the clashes overnight.
Hadi appeared to be under house arrest, the official said.
However, Mohammed al-Bukhaiti, a member of the Houthi politburo, told Reuters: "President Hadi is still in his home. There is no problem, he can leave."
The Houthis appear to hold de facto power over the capital and most of the country after months of territorial gain that culminated in the capture of Sanaa last September.
However, the international community is standing by Hadi as the legitimate leader of the mainly Sunni Arabian Peninsula country.
Peter Salisbury, a Yemen analyst, said it remains unclear how the ultimatum will affect the position of Hadi.
Cristian Barros Melet, Chile’s permanent representative to the UN and currently UN Security Council president, urged all parties to commit to dialogue after a closed Security Council session on Tuesday.
Source: Al Jazeera and agencies