Advani, who was Deputy Prime Minister and Home Minister in the NDA government, talked to Chidambaram over phone.
Sources close to Advani said Chidambaram told him that investigations were on but they were yet to arrive at any "theory" about who could be involved.
Indian Mujahideen claimed responsibility for the attack in an e-mail to several news organisations.
Motorcycle-borne assailants had fired several rounds at a vehicle carrying foreign tourists, injuring two Taiwanese, near the mosque this morning.
Chidambaram told Advani that the Union government was not taking any chances and both Delhi and Mumbai have been alerted after the attack.
Advani also discussed the grave situation in Uttarakhand arising out of incessant rains.
"He demanded that the disaster management authorities should be alerted and all necessary steps should be taken," a source said.
The senior BJP leader had also talked to Uttarakhand Chief Minister Ramesh Pokhriyal Nishank about the situation in the state and the measures being taken.
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