Mr. Danish, the ministry spokesman, said the assailants had been in vehicles that made it seem as if they were from the international coalition.
The Interior Ministry is in charge of the police and other law enforcement agencies. The facility that was attacked on Wednesday opened last year, partly replacing the old ministry in the center of Kabul. That facility was attacked in February by suicide bombers in ambulances who killed more than 100 people, many of them police officers.
In Logar Province, just to the south of Kabul, insurgents mounted an early morning attack on Wednesday against the First District Police Headquarters in the provincial seat of Pul-i-Alam, using a suicide car bomb followed by three gunmen, according to Afghan police officials.
Three officers were killed, including the district’s well-regarded police chief, Khan Agha, and four others were wounded, said Shahpoor Ahmadzai, the spokesman for the Logar police.
“It was 5 in the morning when the Taliban exploded a car bomb near the First District Police Headquarters and three suicide attackers entered the building,” Mr. Ahmadzai said. “The police easily, in 10 or 15 minutes, killed all three of them.”
Eight civilians were also wounded in the attack, Mr. Ahmadzai said.
A spokesman for the Taliban, Zabihullah Mujahid, quickly claimed in a Twitter message that his organization had carried out the Logar attack, but said nothing of the ministry attack claimed by the Islamic State. The Islamic State is much smaller in Afghanistan than the Taliban, but in recent months it has carried out numerous suicide attacks, especially in Kabul.