It was the second attack in days claimed by IS in the city of 200,000 people that was recaptured by government forces from the rival jihadists of Al-Qaeda with US backing.
The suicide bomber killed at least 41 police recruits on the southwestern outskirts of the city, the capital of Hadramawt province, medics said after earlier giving a toll of 31 dead.
The bomber detonated an explosives belt as he joined a line of men at a police recruiting centre, a provincial official said.
More than 60 people were also wounded in the attack in Fuwah district, a medical source said.
Hadramawt’s security chief, General Mubarak al-Oubthani, who was at the recruitment centre at the time of the attack but was not hurt, was the target of a second bombing when he headed into central Mukalla afterwards, a security official said.
The bomb exploded as Oubthani walked out of his office, killing six of his guards but leaving him with only minor injuries, the official said.
An IS statement posted online claimed the suicide attack, a second rare intervention by the militant group in an area known to be a stronghold of its Al-Qaeda rivals.
Brother Abu al-Bara al-Ansari… detonated his explosives belt at a gathering of the apostates of the security forces, it said.
On Thursday, 15 soldiers were killed in jihadist attacks outside Mukalla.
IS said one of its militants blew up a vehicle packed with explosives in an army base in Khalf district on the city’s eastern outskirts.
The attacks included a suicide bombing that targeted the residence of the commander of Hadramawt’s second military region, General Faraj Salmeen, but he escaped unharmed, officials said.
Suspected suicide bomber
On Sunday, troops guarding an army post in Khalf opened fire on a vehicle after they suspected its driver of being a suicide bomber, a security official said, adding the vehicle sped away.
The general boasted on Friday that his forces had captured some 250 Al-Qaeda members since they retook Mukalla and nearby coastal towns, including its commander for the city of Shihr, some 60 kilometres to the east.
Al-Qaeda was driven out of the area last month with the backing of Emirati and Saudi special forces.
The Pentagon revealed last week that a very small number of US military personnel had also been deployed around Mukalla in support of the operation.
The US Navy has several ships nearby, including an amphibious assault vessel, USS Boxer, and two destroyers.
The offensive against Al-Qaeda comes amid a truce and peace talks between the government and Iran-backed rebels it has been fighting with support from a Saudi-led coalition since March last year.
Speaking in Kuwait, the UN special envoy to Yemen said he was optimistic despite unresolved difficult matters.
Now, we have an opportunity to reach a peaceful settlement… the progress we have made on some points makes us optimistic, Ismail Ould Cheikh Ahmed told a news conference.
But there remains some difficult matters… the problem is reaching a clear political agreement.
Special coverage on China's Two Party Sessions by The Daily Mail - People's Daily