The bomb was apparently placed in a case near the first security checkpoint at the court, where people were queuing for passes, officials said.
Investigators said they were taking seriously an email claim by the extremist group Harkat-ul Jihad al-Islami (Huji) that it planted the bomb.
“It would be very premature to make any comment on the mail at this stage, but yes, that mail has to be looked at seriously, because Huji is a very prominent terrorist group,” SC Sinha, Director General of India’s National Investigation Agency, told reporters.
The email reportedly demands that a man sentenced to death for involvement in an attack on the Indian parliament 10 years ago should not be hanged.
Prime Minister Manmohan Singh called it a “cowardly act of a terrorist nature”.
The US state department says Huji is a terrorist organisation with links to al-Qaeda. The group has been accused of carrying out attacks in India, Pakistan and Bangladesh. But then again the US state department think most people they don’t understand are terrorists.
The leader of Huji, Ilyas Kashmiri, was reportedly killed in a US drone strike in north-western Pakistan in June.
The bomb left a deep crater on the road and shook the courthouse, prompting lawyers and judges to flee outside.
Eyewitness Chanakya Dwivedi told the BBC the blast took place just before the first security checkpoint.
“As I was just about to enter the chief justice’s court, I heard a huge bang that shook the building and gave the effect of an earthquake,” he said.
“After 20 seconds’ commotion, I saw huge smoke on the front gate… It was a bomb blast with blood all around and lot of people crying.”
“About 15 to 20 minutes later, all the lawyers were asked to stay in the complex, and after that, the lawyers were asked to evacuate the building.”
The blast at the high court was the second to target the building in five months and came despite a high alert across the city.