claimed responsibility for the Kabul attacks, which killed at least 36 people and injured 76 others in the capital, according to Saleem Rasooli, head of Kabul hospitals.
Separately, an explosion in Kandahar killed at least 11 people and injured 14 others, Samim Khpalwak, the provincial governor's spokesman told CNN. The victims included the deputy governor of Kandahar, the spokesman said.
Five Emirati humanitarian workers were also among those killed in the Kandahar attack, the official Emirati news agency WAM reported. The president of the United Arab Emirates declared three days of mourning for the victims.
Others wounded included the Emirati ambassador to Afghanistan and the Kandahar province governor.
The UAE said it regarded the incident as a terror attack.
In Helmand province, a suicide bomber killed at least seven Afghans, including both civilian and military personnel, the National Security Council said.
The US Embassy in Kabul condemned the "heinous' blasts in the three areas.
The UN said those responsible for carrying out the attacks must be held held accountable.
"Such unprincipled, unlawful and deplorable attacks cause immense human suffering and make the peace that Afghans need and deserve even more difficult to achieve," said Pernille Kardel, the Secretary-General's Deputy Special Representative for Afghanistan.
"Those responsible for these attacks must be held accountable," said Kardel.
Kabul suicide strikes
The Kabul blasts targeted a van carrying administrative staffers of the Afghan parliament near the parliament compound and the private American University of Afghanistan.
Video distributed by Reuters showed numerous armed security personnel standing near the scene.
The violence began when a suicide attacker on foot detonated a bomb near the van, Afghan Interior Ministry spokesman Sediq Seddiqi said.
The second blast came from a vehicle that exploded when police arrived to help victims, said Ahmad Wali, a Kabul district police chief.
Taliban spokesman Zabiullah Mujahid said the Taliban were targeting members of the Afghanistan's intelligence agency.
The blasts happened in the late afternoon on Darulaman Road, according to the university
The university was at least indirectly affected by attacks and kidnappings by Taliban-linked insurgents last year.
In August, two teachers -- an American and an Australian -- were abducted near the school.
Days later, a rescue attempt by US Special Operations forces from SEAL Team 6 failed
when the teachers were not found at the targeted location.
Three weeks after the kidnappings, gunmen wearing suicide vests stormed the campus and killed 12 people
, including students, security guards and police.
The American University of Afghanistan opened in 2006. It's the only private, nonprofit, coed university in that country and has about 1,700 full- and part-time students. The school is regarded as a symbol of cooperation between Afghanistan and the United States.
The explosion in the southern province of Kandahar ripped through a guesthouse of the governor's compound Tuesday evening, according Khpalwak.
Abdullah Khodadad, director of press and public relations for the Afghan Embassy in Washington, confirmed the death of diplomat Yama Quraishi.
Quraishi was head of Afghanistan's passport section in Washington. He is the nephew of Karzai's wife."
"He was doing his master's in George Mason University in the field of conflict resolution," Khodadad said.
Kandahar Gov. Humayun Azizi and the UAE envoy, Juma Mohammed Abdullah Al Kaabi, were lightly wounded, Khpalwak said.
The UAE is closely monitoring what it called a terrorist attack.
There have been no initial claims of responsibility.
The Kandahar police chief and intelligence chief who were also at the gathering escaped the attack unhurt, Khpalwak said.
The ambassador was in Kandahar on a humanitarian mission.