The car bombing occurred on Sunday around 4.30 p.m. near the office of former intelligence chief Amrullah Saleh, who is also Ashraf Ghani's running mate in the presidential elections on September 28.
Three other attackers rushed into the four-storey building and were holed up for several hours as security forces launched an operation that lasted until close to midnight.
"As a result of this attack, 20 people were martyred and another 50 people were injured. Four security forces are among the martyred persons," Interior Ministry spokesperson Nasrat Rahimi told EFE.
All four attackers three assailants and one suicide bomber were killed in the attack, taking the total death toll to 24.
The Interior Ministry is conducting an investigation into the incident, the spokesperson added.
The security forces rescued 150 people who were trapped in the building.
"My brother, true son of the Afghan soil and first VP candidate of my electoral team, @AmrullahSaleh2 has survived a complex attack by enemies of the state," tweeted Ghani.
The attack occurred as the campaign for the presidential elections kicked off on Sunday, as Ghani seeks another term.
The September elections, the fourth since the Taliban regime was overthrown by an invasion by the US in 2001, come amid peace talks between Washington and the insurgents.
The Afghan Taliban on Sunday confirmed it would hold negotiations with the government once it reached an agreement with the US over the withdrawal of its troops from Afghanistan, a day after Kabul announced that negotiations with the rebels would start in two weeks.
The US special envoy for Afghan reconciliation said earlier on Sunday that peace talks between the government and the Taliban would take place only after Washington ended its own negotiations with the militant group.
Despite the ongoing talks, violence has continued across the country, with at least five attacks recorded in Kabul over the past week, resulting in 14 deaths.
( With inputs from IANS )