At least 47 people have been killed in a suicide bomb attack on supporters of a Shia rebel group in the centre of Yemen's capital, Sanaa, reports say.
The blast struck as hundreds of people were arriving in Tahrir Square for a demonstration called by the Houthis.
Later, a suicide bomb attack on an army checkpoint in the eastern province of Hadramawt left 20 soldiers dead.
The attacks come amid a deepening political crisis triggered by the rebels' takeover of Sanaa last month.
The Houthis have rejected the president's candidate to lead the new government which is meant to be formed as part of a deal that brought an end to the deadly fighting between the Houthis and government forces.
The bombing in Sanaa appeared to have been timed to cause a big loss of life and was the deadliest in the capital since May 2012.
A policeman who had been guarding a bank near Tahrir Square said he saw a man wearing an explosive belt approach a Houthi checkpoint.
"He then exploded amidst the [Houthi] security and ordinary people nearby," he told the Reuters news agency.
A photographer working for AFP described seeing the bodies of four children amid the carnage. Medics said at least 75 people were also wounded by the blast.
At a subsequent meeting with foreign ambassadors in Sanaa, President Abdrabbuh Mansour Hadi condemned what he called the "coward terrorist bombing", the official Saba news agency reported.
In the Hadramawt attack, a tank and two army vehicles were destroyed when a suicide bomber blew up his explosives-filled car at a checkpoint on the outskirts of the port city of Mukalla.
No group has said it was behind Thursday's bombings, but both bear the hallmarks of previous attacks by al-Qaeda in the Arabian Peninsula (AQAP), which has vowed to fight the Houthis in defence of Sunnis.
On Wednesday, officials accused the jihadist group of responsibility for simultaneous attacks on security and government offices in the southern town of Bayda that left at least nine people dead.
Thursday's demonstration was called by the Houthis to protest against President Hadi's nomination of Ahmed Awad bin Mubarak for the post of prime minister.
Mr Mubarak asked the president early on Thursday to relieve him of the post, saying he wanted to "preserve national unity", but hundreds of Houthi supporters still rallied to show their anger.
On Wednesday night, rebel leader Abdul Malik al-Houthi said in a televised address that his group had been surprised by Mr Bin Mubarak's nomination.
The move had been announced on Tuesday after the president met the US ambassador to Yemen, he added.
He called Mr Hadi a "puppet" and warned: "Blatant foreign interference is a form of circumventing the popular revolution."
Under a deal brokered by the UN after the Houthis took control of Sanaa on 21 September, Mr Hadi agreed to reverse unpopular fuel subsidy cuts, form a new "technocratic national government", and appoint advisers nominated by the rebels and the separatist movement in the South.
In return, the rebels were to withdraw from Sanaa and other northern cities, and hand over their weapons to the authorities within 45 days. However, armed Houthis were still deployed in the capital on Thursday.
The Houthis, who adhere to a branch of Shia Islam known as Zaidism, have staged periodic uprisings since 2004 in an effort to win greater autonomy for their northern heartland of Saada province.
Opponents allege that the rebels ultimately hope to reinstall the Zaidi imamate, which ruled North Yemen for almost 1,000 years until 1962.