Kabul Attack Network is prime suspect in InterContinental Holel attack

This is still such a fast-moving story it can't be established at this time with any certainty which group carried out the attack but Long War Journal's June 28 discussion provides the best guess at this time as to the identity of the perpetrators' gang. See the LWJ website for source links in the report:

[...] Today's suicide attack was likely carried out by the Kabul Attack Network, which is made up of fighters from the Taliban, the Haqqani Network, and Hizb-i-Islami Gulbuddin, and cooperates with terror groups such as the Lashkar-e-Taiba and al Qaeda.

Top Afghan intelligence officials have linked the Kabul Attack Network to Pakistan's Inter-Services Intelligence directorate as well. The network's tentacles extend outward from Kabul into the surrounding provinces of Logar, Wardak, Nangarhar, Kapisa, Ghazni, and Zabul, a US intelligence official told The Long War Journal.

The Kabul Attack Network is led by Dawood (or Daud) and Taj Mir Jawad, military and intelligence officials told The Long War Journal. Dawood is the Taliban's shadow governor for Kabul, while Taj Mir Jawad is a top commander in the Haqqani Network.

The Taliban have prioritized attacks against hotels in Kabul. In February, a suicide bomber detonated at the Safi Landmark. And in January 2008, a suicide assault team carried out an attack similar to today's at the Serena Hotel. Foreigners were the targets of both strikes.

Today's attack is the second major strike in Kabul this month. On June 18, a heavily armed three-man-strong suicide assault team dressed in military uniforms attacked a police station in the 1st district in Kabul, near the Finance Ministry. Nine people were killed in the attack.

The Taliban have carried out two other major suicide attacks in the capital since the beginning of April. On May 21, a suicide bomber detonated his vest at a hospital that is used to treat Afghan soldiers. Six people were killed in the blast. And on April 2, a suicide assault team attempted to storm Camp Phoenix, a NATO base. The suicide bombers were defeated by US troops guarding the perimeter.