The Economic Offences Wing (EOW) of Delhi Police has launched a probe into the matter after registering an FIR on March 2 on the basis of Khurshid's complaint.
Police said Khurshid came to know about sale of the puppies while surfing through the portal on February 13. The advertisement had quoted the price of two puppies at Rs 12,000 each.
The former external affairs minister contacted over email the accused, Tonny Wallace, who claimed to be in Thekkad, Kerala.
Following the email correspondence till February 19, a representative from Khurshid's office started interacting with Wallace, who asked him to transfer the money in the account of one Ankit Badri, also named in the FIR along with him.
After Khurshid's representative transferred Rs 59,000 to Badri's account, Wallace told Khurshid that he would be available on his US toll free number and on Facebook.
The accused then demanded more money from the Congress leader on the pretext of health checks and health certificate of the puppies and their transportation to Delhi.
Later, Wallace told the minister that the pets will be delivered to Delhi through a pet travel agency - Pacific Pet Re-Locators - but they were never delivered.
Khurshid filed the complaint on February 21 with the Barakhamba Road police station and subsequently the matter was transferred to the EOW.
Police said they have begun a probe in the matter and are trying to identify the accused through the bank account details and the Facebook page link shared by Khurshid.
The former Union minister also alleged in the complaint that the accused "transact in online trading of Bitcoins wherein they lure online purchasers through advertisements on e-commerce websites".
Khurshid said they investigated the matter at their end and have provided all the details to the investigators.
"The cyber world is full of pitfalls and ensuring cyber security is a huge problem. I hope that the police that is engaged in looking after cyber crime will be able to get to the bottom of this," he said.
While the Congress leader's complaint mentions about the Bitcoin trade, the FIR registered by EOW does not mention it.
"Bitcoin trade is a worrisome thing because it is anonymous and because it is used world over for nefarious things. If we are aren't alert now, something might happen.
"It will come out. We are giving them (police) some time," the former Union minister added.