Troops engaged the attackers while evacuating lawmakers and staff members from the Parliament complex. Almost two hours after the attack began, officials told the media that all the attackers had been killed by special forces.
Interior ministry spokesperson Sediq Sediqqi tweeted that Afghan Police had repelled the attack and killed the seven attackers. He added no MP was wounded.
Women and children were among the 31 people wounded, health ministry officials said.
Indian nationals working on a new parliament building nearby were reported to be safe, Hindustan Times reported.
"A suicide bomber blew himself up just outside the parliament building and several fighters took positions in a building close to Parliament," Ebadullah Karimi, spokesperson for Kabul police, said shortly after the assault began.
The bomber detonated his explosive-laden car on the busy Darul Aman road near the gates of Parliament, damaging other vehicles and nearby buildings. This was followed by more than half a dozen blasts and the attackers exchanged fire with security personnel who converged on the site.
In a message sent to the media, Afghan Taliban spokesperson Zabihullah Mujahid said suicide bombers had carried out the attack. The Taliban described it as a “coordinated suicide attack”.
Mujahid said: "We have launched an attack on parliament as there was an important gathering to introduce the country's defence minister."
The explosions occurred as the new defence minister, Masoom Stanekzai, was being introduced to MPs for a vote of confidence.
Parliamentarian Harif Rahmani, who was inside the Wolesi Jirga or lower house of parliament at the time of the explosions, told Tolo News channel the MPs were evacuated without serious injuries.
Rahmani said the gunmen were unable to enter the parliament because of the strong security presence.
Lawmaker Shukria Barekzai said: "It was a huge blast that shook the building and shattered windows. We are in a safe place right now."
Dramatic footage aired on TV channels showed MPs screaming after a blast went off as the lower house was in session. The room rapidly filled with smoke as security personnel began escorting the MPs out. Footage on television also showed a car on fire on the road outside the parliament compound, smoke billowing into the sky, agencies reported.
The attack on Parliament came as a second district fell to the Taliban in the north in two days. The Taliban captured Dasht-e-Archi district a day after hundreds of militants took control of the adjacent district of Chardara.