An Indian army spokesman confirmed the Thursday attack on the anti-resistance training school in the town of Khrew, to the south of Srinagar in the Pulwama district.
One of the attackers was shot dead and two Indian soldiers were wounded, but fatalities look set to rise as the spokesman said fighting around the school continued.
An anonymous call to a local newspaper office in Srinagar said the Pakistan-based Jaish-e-Muhammad were claiming responsibility for the attack.
Jaish-e-Muhammad emerged out of Harakat al-Mujahidin in the months following the hijack of an Indian Airlines plane from Kathmandu in December 1999.
The hijackers demanded the release of three militant leaders, two of whom later became leading figures in the group.
India blames Jaish for an attack on its parliament in Delhi in December 2001.
The group denies the charge but the attack led the US State Department and the Pakistan Government to impose a ban on it for alleged terrorist activities.
Jaish-e-Muhammad is believed to have been started by a Muslim cleric, Mawlana Masud Azhar.
Another prominent member is English-born Shaikh Umar, who studied at the London School of Economics for a year.
Pakistani police suspect Daniel
Peal was executed by Jaish
Pakistani police have hunted for Umar who they are reported to believe is directly involved in the kidnapping of Wall Street Journal correspondent Daniel Pearl.
Jaish-e-Muhammad literally means the Army of Muhammad.
Largely based in Pakistan, the group has been linked to a string of violent attacks in India, especially in Indian-administered Kashmir.
It claims to be fighting what it describes as a holy war and aims to overthrow Indian rule in Kashmir.
Azhar was placed under arrest after the Pakistani President, Pervez Musharraf, banned the Jaish group in 2002.