Amid reports of Ali Abdullah Saleh's possible return to Yemen, the US has called for an "immediate transition" of power.
Speculation is rife that the Yemeni president's stay in Saudi Arabia, where he had surgery for shrapnel wounds suffered in an attack on his palace on Friday, might be prolonged as the kingdom tries to negotiate a power-transition deal.
"We think an immediate transition is in the best interests of the Yemeni people," Hillary Clinton, secretary of state, said on Monday.
For her part, Catherine Ashton, the European Union's foreign policy chief, said she hoped Saleh would let his country "move on" while he sought medical treatment in Saudi Arabia.
More than 450 people have been killed in the unrest shaking the nation of 23 million since late January.
The US fears that al-Qaeda's branch in Yemen could exploit the turmoil to strengthen its presence in the country, which it has already used as a base for plotting two attempted anti-US attacks.
Earlier on Monday, Abdu-Rabbu Mansour Hadi, Yemen's acting leader, was quoted as saying on the Saba state news agency that Saleh's health was improving and he "would return to the homeland in the coming days".
A Saudi-negotiated truce was holding in Sanaa, the Yemeni capital, after two weeks of fighting between Saleh's forces and a powerful tribal group in which more than 200 people were killed and thousands fled.
Risk of unravelling
The Saudi-led Gulf Co-operation Council urged all parties to work to end violence and said it was continuing its efforts to negotiate a power-transfer deal.
But the ceasefire in Sanaa was at risk of unravelling on Monday as government supporters opened fire on opposition fighters in renewed clashes that killed at least six.
Youthful protesters, interpreting Saleh's absence as potentially permanent, continued to celebrate in Sanaa where they have staged anti-government demonstrations since January.
"It's impossible for us to let [Saleh] come back. And those of his people who are still here had better follow him to Saudi," said one of those attending a Sanaa rally.
"Who is next?" asked one banner held up by protesters in a sea of red, white and black Yemeni flags, referring to the wave of uprisings in the Arab world and north Africa that has toppled the leaders of Egypt and Tunisia and inspired revolts in Syria, Libya and Bahrain.
Saleh's departure could make it hard for him to retain control, although his close relatives still command key military units and security forces.
Saleh, a political survivor, has defied global calls to step down and survived the defection of top generals, ministers and ambassadors.