Interior Ministry spokesman Najib Danish said the Kabul attack took place in the Shash Darak area near NATO headquarters and not far from the U.S. Embassy. Danish said the initial casualty count could rise.
The Islamic State group in a statement on its website claimed responsibility.
U.S. Gen. John Nicholson, commander of Resolute Support Mission in Afghanistan, said at a news conference he expected IS and the Taliban to continue such attacks.
"We will work hard with our Afghan security counterparts and teammates to help protect the civilians of Afghanistan as much as possible," he said.
In western Farah province, at least 18 soldiers were killed when their checkpoint came under attack by Taliban insurgents, said Dawlat Waziri, spokesman for the Defense Ministry. He said two other soldiers were wounded in the attack in the Bala Buluk district.
Qari Yusouf Ahmadi, a Taliban spokesman, claimed responsibility for the attack in a statement.
Meanwhile, an Afghan official said at least three security personnel were killed in separate suicide bombing attacks in southern Helmand province.
Omar Zwak, spokesman for the provincial governor in Helmand, said a car bomber early Saturday was shot by Afghan army soldiers but his vehicle managed to reach the entrance of the army base in Nad Aali district, killing two soldiers and wounding another.
In a second suicide bombing attack near another military base in Helmand's capital city Lashkar Gah, one security person was killed and seven civilians wounded, Zwak said.
Qari Yusouf Ahmadi, a Taliban spokesman, claimed responsibility for both suicide attacks in Helmand.
The resurgent Taliban and the newer IS affiliate have been blamed for increased violence in Afghanistan after U.S. and NATO forces concluded combat missions in 2014 that began after the 9/11 attacks in the U.S.
On Jan. 27, a Taliban attacker drove an ambulance filled with explosives into the heart of the city, killing at least 103 people and wounding as many as 235.
The Taliban claimed the ambulance attack, as well as an attack a week earlier in which militants stormed a luxury hotel in Kabul, killing 22 people, including 14 foreigners, and setting off a 13-hour battle with security forces.
The recent attacks have underscored the weaknesses of Afghan security forces more than 16 years after the U.S.-led invasion toppled the Taliban.
They also raise questions about President Donald Trump's strategy for winning America's longest war, which was announced in August but has changed little on the ground. That strategy was based on ramping up military pressure on the Taliban to eventually force them into peace talks with the government.
Associated Press writers Mirwais Khan in Kandahar and Maamoun Youssef in Cairo contributed to this report.
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