The first explosion happened in Shashdarak area of Kabul, near the U.S. embassy and Afghan government buildings.
A second blast came when an attacker, posing as a cameraman, detonated explosives -- killing at least eight journalists, officials said.
The Islamic State later took credit for the attack.
Radio Free Europe said three of its journalists -- Abadullah Hananzai, Maharram Durrani and Sabawoon Kakar -- died.
"The targeting of civilians, worshipers in mosques, national and democratic processes, journalists, and freedom of expression are concrete examples of war crimes," Afghan President Ashraf Ghani said in a statement. "This terrorist act is in conflict with Islamic values and human rights."
The U.S. Embassy in Afghanistan condemned Monday's attacks as "savage".
"We mourn for those murdered, including the brave journalists who stand for truth in the face of violence," U.S. Ambassador John Bass said on Twitter.
In recent weeks, other suicide bomber attacks have plagued Afghanistan.
On April 22, an Islamic State suicide bomber killed at least 57 people and injured more than 100 at a voter registration site in Kabul. A day later, coordinated Taliban attacks in two cities killed at least 16 security officers.