Hadi, who had been under house arrest since he resigned under pressure from Houthi rebels in the capital, Sanaa, last month, fled with the help of forces loyal to him at about 4 a.m., one of his advisers said on condition of anonymity.
A senior Houthi official confirmed Hadi's escape. Houthis are working to capture him in Aden, said that official, also speaking on condition of anonymity.
Later Saturday, the news network Al Jazeera reported it received a paper statement from Hadi in Aden -- a statement in which he effectively declared himself to still be President.
According to Al Jazeera, Hadi said all political decisions made since September 21 -- the start of what he called a Houthi coup -- are invalid. That would include his under-pressure resignation.
Details about how Hadi slipped away from house arrest -- he had been under guard by Houthi security personnel -- were not immediately available. No fighting was reported in connection with his escape.
Hadi intends to withdraw his resignation in a televised speech this weekend, two of his advisers said Saturday.
"President Hadi escaped from his residence after the Houthis arrested him and oppressed him and his family," one of the advisers said on condition of anonymity. "He is the constitutional president of Yemen, and he has the constitutional capacity to withdraw his resignation."
Such a move would further complicate the question of who runs the country. The capital has been held for weeks by the Houthis, a minority rebel group that holds sway in the nation's north but has far less influence elsewhere.
Hadi and Prime Minister Khaled Bahah resigned in January under Houthi pressure, a few months after the rebels entered the capital with guns blazing, demanding greater political influence.
Houthis are Shiite Muslims who have long felt marginalized in the majority Sunni Muslim country. They had been at war with the central government for more than a decade, but their entry into Sanaa in September brought things to a head, sparking battles that left than 300 people dead before a ceasefire was agreed that month. Houthis then pressured Hadi and Bahah to step down last month after the pair refused to agree to certain political demands.
The Houthis' takeover of Sanaa stunned governments of Western nations, which, along with other countries, pulled out diplomatic staff this month.
Houthis arrest own security personnel after escape
As part of an investigation into Hadi's escape, Houthis on Saturday arrested dozens of their own security personnel who were responsible for watching him, the senior Houthi official said.
Houthis arrested two people connected to Hadi -- his media secretary Yahya Al Arassi and Hadi's private physician -- after his escape, one of Hadi's advisers said.
A senior official with a Sunni political party opposed to the Houthi takeover said that he backs Hadi's claim to the presidency.
"Hadi's withdrawal (of his resignation) would save the country and end the Houthi oppression of the Yemeni people," said Mohammed Al Sabri, senior official of the Nasserite party.
Houthis have been pressuring the parliament to formally accept Hadi's resignation, a step that has not yet happened. Parliament will do no such thing, prominent lawmaker Abdu Al Huthafi, a Sunni Muslim, said Saturday.
"Hadi informed political alliances ... that he will withdraw his resignation in the right time, and that could be very soon," Al Huthafi said.
Before news of Hadi's escape spread in Sanaa in the late morning, about 6,000 demonstrators marched in Sanaa's streets against the Houthis. Anti-Houthi protests also took place in four other provinces -- Taiz, Ibb, Al Baitha and Dhammar -- protest organizers there said.
There already had been resistance to the Houthis' attempted takeover of national government institutions from different groups in Yemen, particularly in the south, where there's a long-running secessionist movement.
Also opposed to the Houthis are the Sunni terror group al Qaeda in the Arabian Peninsula (AQAP), which exerts influence over many rural areas stretching from the country's southwest to the northeast. AQAP vowed to attack Houthi loyalists nationwide last year.
Yemen's political turmoil could have an impact on the United States' fight against AQAP. The United States has long had a relationship with Yemen's leaders, working with them to target AQAP militants.
It's not clear what the Houthis' takeover of Sanaa means for U.S. anti-terrorism efforts, but the drone program there still appears to be active. A U.S. drone strike killed senior AQAP cleric Harith bin Ghazi al-Nadhari and three other people in Shabwa province on January 31.