The bombings underscored Yemen's highly volatile situation following last month's takeover of the capital, Sanaa, by the Shiite Houthi rebels whose blitz stunned the impoverished Arab nation on the southern corner of the Arabian Peninsula.
The Houthis' push into Sanaa also prompted threats of retaliation from their Sunni militant foes in al-Qaida's Yemen branch.
The Health Ministry said at least 47 people died and 75 were wounded when a suicide attacker set off his explosives today morning in central Sanaa.
The officials spoke on condition of anonymity because they were not authorised to talk to media.
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The second bombing took place on the outskirts of the southern port city of Mukalla in Hadarmout province when a suicide car bomber rammed his car against a security outpost, killing at least 20 soldiers and wounding 15, the officials said.
Hadarmout is one of several strongholds of al-Qaida's Yemeni branch, considered by Washington to be the most dangerous offshoot of the terror network.
In Sanaa, the dead and wounded were taken to three hospitals. At one of them, the Al-Moayed hospital, victims' body parts were piled up on the hospital floor, and two severed heads were placed next to two headless bodies.
The body of a man was placed nearby, one of his legs next to it. There were at least six children in critical condition and some of the wounded arrived in hospital badly burnt, missing an eye or a limb.