The suicide bomb attack during the evening rush hour Tuesday outside the court was one of the deadliest in the Afghan capital in which at least 16 people died and more than 40 were injured. CNN put the death toll at 17.
The attack site is in the center of Kabul where the U.S. Embassy and the headquarters of NATO's International Security Assistance Force are located.
The BBC, quoting police, said the attacker set of the explosives in his vehicle at buses transporting court employees and judges.
The BBC reported a Taliban statement it received said it killed judges who "obey Western powers."
CNN quoted Taliban spokesman Zabiullah Mujahid's emailed statement as saying government judges are oppressing and mistreating people in several parts of the country. The militant group claimed its members had been following Supreme Court judges and high-ranking staff members for some time prior to the attack
CNN quoted a police official that two women and three children were among the 17 people killed. Those injured included eight women.
Condemning the attack, Gen. Joseph Dunford, commander of NATO's ISAF, said: "Once again the enemies of Afghanistan have demonstrated a complete lack of respect for human life. ... The targeting of hard working Afghans on their way home from work is reprehensible."
The bomb was set off near Masoud Circle, designed to cause the maximum number of civilian casualties, the ISAF said.
Khaama Press quoted witnesses that at least three vehicles carrying Supreme Court employees were damaged.
The bombing in the Afghan capital came a day after seven heavily armed Afghan insurgents, two of them suicide bombers, took over two buildings under construction near Kabul airport. All seven later died while fighting security forces, officials said.
The Taliban already has announced the start of their so-called spring offensive against foreign military forces, which are due to end their combat operations by the end of next year. Taliban insurgency in Kabul has escalated, apparently to show to the world the group's strength has not been affected by the coalition forces, the report said.
CNN said at least 18 coalition soldiers have died in June alone in the various insurgent attacks across the country this spring. In May, a suicide car bombing on a coalition convoy in central Kabul killed at least 12 people, six of them Americans.