He said in a statement that "security forces have the ability to protect the lives and property of the people of Afghanistan".
Holbrooke's visit to Kabul, which is part of a broader tour of the region, comes as Barack Obama, the US president, focuses on combating Taliban and al-Qaeda linked fighters based in Pakistan and Afghanistan.
"The information we are getting is that the events on Wednesday have no bearing on Holbrooke's travel plans," Hamish MacDonald, Al Jazeera's correspondent in Kabul, said.
"But clearly, if those events are not affecting his plans, they will certainly affect the meeting he will hold. He will surely be asking leaders here why they cannot even secure government infrastructure in the capital."
Washington has already said that it will send thousands of extra troops to Afghanistan to help Kabul fight the Taliban, which has been resurgent in the last few months.
The most deadly attack in Kabul on Wednesday took place at the justice ministry, where armed men killed at least 10 ministry employees, Atmar said.
Five attackers were shot dead and three died after they detonated bombs.
A Taliban spokesman told Al Jazeera that the attacks were aimed at avenging the mistreatment of some of its men held in Afghan jails.
The Afghan government has in the past blamed attacks in the country on Taliban and al-Qaeda-linked fighters based in Pakistan's tribal areas over the Afghan-Pakistani border.
Most of the fighters there are thought to be those who fled Afghanistan during the US-led invasion of the country in 2001.
The attacks on the Afghan capital underscore the depth of the security challenges facing nearly 70,000 US and international troops stationed across the country.
Obama is expected to approve the deployment of about 30,000 extra troops to Afghanistan in the next few days.