Authorities said they were trying to pin down the location of the third blast and there was no immediate claim of responsibility from any militant group.
Kabul attack death toll 24, with 91 wounded
It jolted the capital just hours after high-level officials, including an army general, were killed in the twin blasts near the defence ministry, as the Taliban ramp up their nationwide offensive against the US-backed government.
A suicide bomber struck the area just minutes after the first explosion, in an assault apparently aimed at inflicting mass casualties as officials left the ministry after work.
"The first explosion occurred on a bridge near the defence ministry. The second struck just as soldiers, policemen and civilians hurried to help the victims," defence ministry spokesman Mohammad Radmanish told AFP.
Ambulances rushed to the scene, littered with disfigured bodies and charred debris. But there were so many bodies that some had to be taken to hospitals in car boots and the back of police pickup trucks.
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Firemen, meanwhile, raced to retrieve some bodies thrown into the Kabul River by the intensity of the first blast on the bridge.
Health ministry spokesman Waheed Majroh said the attack left 24 people dead and 91 others wounded, some of them seriously, adding the casualties could rise still further.
The Italian-run Emergency Hospital in Kabul, which was overwhelmed with wounded patients, tweeted that four people died on arrival.
The interior ministry initially said the attack was carried out by two suicide bombers on foot. But officials later said the first bomb was detonated remotely while the second was triggered by a suicide bomber.
Taliban spokesman Zabihullah Mujahid said on Twitter that the defence ministry was the object of the first attack, while police were targeted in the second.
President Ashraf Ghani strongly condemned the carnage and offered condolences to the families of the victims.
"The enemies of Afghanistan have lost their ability to fight the security and defence forces of the country," Ghani said in a statement.
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"That is why they are attacking highways, cities, mosques, schools and common people."
The attack took place more than a week after 16 people were killed when militants stormed the American University of Afghanistan in Kabul, in a nearly 10-hour raid that prompted anguished pleas for help from trapped students.
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