In a statement read over the phone to Kashmir's Current News Service, a man who identified himself as Abu al-Hadeed, reportedly said: "whosoever has carried out the attacks in Bombay we express our gratitude and happiness."
The Bombay train bombings on Tuesday killed at least 200 people and injured more than 700. Kashmiri militants are being investigated for the attack, although two main rebel groups have denied responsibility.
He said the Bombay bombings "are a reaction to what is happening to the minorities, especially Muslims in India."
It was impossible to immediately verify the man's identity and if he actually represents a new wing of Al Qaeda.
There have been allegations that Islamic militants fighting to wrest predominantly Muslim Kashmir from India have ties to Al Qaeda, but Thursday's statement is the first time Usama bin Laden's network has claimed to have spread to Indian territory.
"We appeal to Muslims in India to fight for freedom and Islam and choose jihad as their way to achieve freedom and establishing Islamic ways," al-Hadeed was quoted as saying.
"We shall be giving out statements regularly and will soon announce our aims and objectives," he was quoted as saying.
Al-Hadeed identified the network's Kashmir leader as Abu Abdul Rehman al-Ansari. Both names are Arabic, not Urdu, the language spoken most of the sub-continent's Muslims.
Current News said al-Hadeed spoke in Urdu. But he reportedly said: "Henceforth our statements will be in Arabic."