The email, which said the militant group Harkat-ul-Jihad al-Islami (HuJI) carried out the September 7 attack, was traced to an Internet cafe in Kishtwar, near the Kashmiri city of Jammu.
Police, who identified the two students as Abid Hussain and Sharik Butt, said investigators were unable to confirm whether the email was a genuine claim or a hoax.
"We have arrested two people suspected of sending the email," a police officer told AFP, declining to give his name. He said the arrests were made a few days ago.
The two, both aged 17 or 18, were tracked down after questioning of the Internet cafe owners and people using its computers when the email was sent.
Another claim of responsibility, apparently from a home-grown militant outfit called Indian Mujahideen, was also sent to media the day after the attack.
HuJI has been accused of carrying out attacks in India, Pakistan and Bangladesh, but the group has not been active in Muslim-majority Kashmir for years.
Last week's blast ripped through a crowd queuing to enter the court complex in the heart of the Indian capital. Eleven people were killed on the spot while two more died later in hospital from their injuries.
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As usual probe going nowhere.