The International Security Assistance Force called the attack "senseless and cowardly." The military officials said in a release that the bombing killed at least 19 people and wounded more than 43 others.
"These despicable acts continue to disrupt peace and demonstrate an utter lack of respect for Afghan lives," the ISAF statement said.
Marine Corps Gen. John R. Allen, the ISAF commander, blamed the attack on the Taliban and said it was a case of murder "in cold blood."
"Their depravity clearly knows no bounds. The disgust of the Afghan people for these criminals only continues to grow," he said.
"ISAF continues to stand with the noble people of Afghanistan and we offer our assistance in solving this crime. I offer my sincerest condolences and prayers to the family and friends who are suffering from the loss of their loved ones."
A Taliban spokesman denied the Islamist group was involved in the attack, the BBC reported.
Ahmad Khan Samangani, an ethnic Uzbek member of Parliament, was attending a wedding party for his daughter in Samangan's provincial capital, Aybak, when the blast occurred, the BBC said.
The attacker had posed as a guest and embraced Samangani, then detonated his explosives, a witness said.
Samangani was a commander in the mujahedin militia during Afghanistan's civil war in the 1980s.
Samangani became a member of Parliament last year.
A statement from Karzai's office blamed "enemies of Afghanistan" for the attack, and Karzai has appointed a team to investigate.
Meanwhile, authorities said gunmen killed the security chief for the 15th district in Kandahar city in the southern province of Kandahar Saturday.
Authorities said Misteri Rahmatullah was on his way to work when he was shot about 9 a.m., Khaama Press reported.
Afghan security forces were searching for the gunmen, provincial governor spokesman Javid Faisal said.
On Friday, Kandhar provincial police chief Gen. Abdul Razaq said, militants killed three Afghan civilians in the Shahwali-Kot district for supporting the Afghan government.
Razaq said security forces had killed three Taliban militants Friday in the Shahwali-Kot district.