Deependra Pathak, Joint Commissioner of Delhi Police said: "The Cyber Cell has lodged two FIRs in the hacking case. We are probing the matter."
"We are also taking help from officials in Twitter in Bengaluru," he added.
The cases were registered under Section 66 of IT Act following complaints from the Congress party leaders.
On Wednesday night, Mr Gandhi's Twitter account was hacked and expletives and abuses were posted on it. The same account was hacked again on Thursday morning.
A few hours later, the Congress party's official Twitter account was found to be hacked as well.