SANAA, Yemen — Thousands of Yemenis rallied in support of rival political groups Friday and separatist groups in the south pressed for secession following the government’s resignation in response to a siege by Shiite rebels.

The decision Thursday by President Abed Rabbo Mansour Hadi and his cabinet to step down produced more uncertainty over the future of this desperately poor and divided nation, which hosts a powerful al-Qaida affiliate.

It was not immediately clear whether the rebel Houthis, members of the Zaydi sect of Shiite Islam, now consider themselves Yemen’s rulers. The rebels besieged the residences of the president and other government officials in this majority Sunni Muslim country this week. The assault was decried as a coup by neighboring Sunni Arab states, which see the insurgents as a client of Iran.

The state-run SABA news agency reported that parliament would convene Sunday to discuss the resignations.

“What we’re feeling is fear and insecurity,” said Hussam al-Qahtani, 22, a university student who lives in the capital, Sanaa. He has stopped leaving the house at night over fear of being caught in the clashes between Houthi fighters and government forces, which have left more than a dozen people dead in the past week.