The bombings underscored the highly volatile situation in Yemen following last month’s takeover of the capital, Sana’a, by the Shia Houthi rebels.
The Houthi push into Sana’a also prompted threats of retaliation from their Sunni militant foes in al-Qaeda’s Yemen branch.
In yesterday’s attacks, at least 47 died and 75 were wounded when a suicide bomber set off explosives in central Sana’a.
The attacker targeted a gathering of Houthis and their supporters, mingling among the protesters as they were getting ready for the rally.
The second bombing took place on the outskirts of the southern port city of Mukalla when a suicide car bomber rammed his vehicle into a security outpost, killing at least 20 soldiers and wounding 15.
The surrounding region is one of several strongholds of al-Qaeda’s Yemeni branch. There was no immediate claim of responsibility for either attack.
In Sana’a, the dead and wounded were taken to three hospitals. There were at least six children in critical condition and some of the wounded arrived in hospital badly burnt and with missing limbs.
At the scene of the blast in Tahrir Street, one of Sana’a’s busiest, blood pooled on the ground as volunteers picked up body parts. Sandals and other personal belongings of the victims were scattered about.
Last week, al-Qaeda in Yemen warned it would target the Houthis and called on the country’s Sunnis to close ranks and fight the Shia rebels.
The Houthis had called the Sana’a rally to protest against president Abed Rabbo Mansour Hadi’s choice of new prime minister, Ahmed Awad bin Mubarak. As the crisis escalated, the prime minister-designate asked Mr Hadi to relieve him of the post.
But, despite the bombing and Mr bin Mubarak declining the premiership, the rally went ahead later, with around 4,000 Houthis calling on Mr Hadi to step down and chanting slogans against the United States and Saudi Arabia.
Rebel leader Abdel-Malik al-Houthi delivered a televised statement on Wednesday night, calling on supporters to rally yesterday against the choice of Mr bin Mubarak.
He said his group was surprised by the nomination, saying it came after Mr Hadi had met the US ambassador to Yemen. Mr Houthi called Mr Hadi a “puppet”.
“Blatant foreign interference is a form of circumventing the popular revolution,” he said.
The Houthis took control of Sana’a last month, but a UN-brokered deal managed to bring street battles in the capital to an end.
The Houthi takeover of Sana’a followed weeks of protests by supporters to press demands for a larger share of power and a change in government.