"Three big bangs" went off at the funeral of Salem Izadyar, the son of Mohammad Alam Izadyar, first deputy chairman of the Afghan Senate, a witness told CNN.
The Taliban denied involvement in the funeral attack, which injured 119 people.
The blasts were from three suicide bombings, said the government's chief executive, Abdullah Abdullah, who attended the funeral and tweeted he was not harmed. Abdullah described the attack on TV, Sune Engel Rasmussen of The Guardian said on CNN.
Lawmakers and high-profile government officials attended the funeral, including those from the senator's Jamiat-e Islami party, Rasmussen said. Jamiat is a largely Tajik political movement and an adversary of the Taliban.
'Bring terrorists to justice'
Afghan President Ashraf Ghani said he and Abdullah "share a commitment" to "bring terrorists to justice." The men are the leaders of Afghanistan's national unity government.
"The country is under attack. We must be strong and united," Ghani said on Twitter.
"There have been too many martyrs, and too much blood spilt," Ghani said in another tweet. "I grieve with the widows and orphans, and pray for those lost."
But a former Afghan intelligence chief, Amrullah Saleh, lashed out at the government for its failure to protect the funeral.
Salem Izadyar died at a hospital after he was injured Friday in anti-government protests in Kabul, Afghan media reported.
Incensed over the Wednesday suicide attack that left 90 dead
in Kabul's diplomatic zone, Afghans took to the streets
Friday to demand government officials step down. There has been no claim of responsibility.
At least four people died in the protests as demonstrators hurled stones and Afghan police fired bullets into the air to try to disperse crowds.
In recent months, the security situation in Kabul and throughout the country has worsened, heightening Afghans' anxiety and despair.
The uptick in violence this week coincides with the Muslim holy month of Ramadan, a time of fasting and contemplation. The Taliban claimed responsibility at the start of the holy period for a car bombing that killed at least 18 people May 27 in eastern Afghanistan.
'Too much civilian suffering'
Tadamichi Yamamoto, UN envoy to Afghanistan, expressed his condolences to the victims of the funeral bombing and condemned the attack as "morally reprehensible."
Yamamoto urged all members of the international community to help put an end to the cycle of violence.
"As I have repeatedly said, the ultimate objective in Afghanistan must be a negotiated peace," he said in a statement. "Meaningful steps must take place now to obtain an immediate, nationwide halt to violence."
The unrest comes as a regional summit is scheduled for Tuesday to promote peace, security and reconciliation. The effort is dubbed the Kabul Process
, and representatives from 21 nations have been invited, according to local news reports.
The conference will be a "visible reminder to all those who seek to harm Afghanistan that the Afghan people are never alone," said Special Charge d'Affaires Hugo Llorens, the top US diplomat to Kabul.
"As always, the United States, along with all of Afghanistan's partners, remains shoulder-to-shoulder with our Afghan brothers and sisters in pursuit of a brighter tomorrow for all Afghans," Llorens said in a statement.