The two are drop-outs of a private college at Jharpokharia in Mayurbhanj district and residents of Ghatsila in Jharkhand, sub-divisional police officer, Baripada, Sudhakar Jena said.
They were detained yesterday and are being interrogated by the police, the SDPO said.
Tudu, who is the Mayurbhanj district president of the BJD, has alleged that he received a series of threat calls purportedly from Maoists.
The mobile SIM used by the duo was issued in the name of one Manas Puhana of Bhanjanagar in Ganjam district. However, their relation with Naxalites was not established during interrogation, he said.
In an FIR at Chandua police station on Wednesday, Tudu had alleged that he had first received a threat call on October 4 where the caller demanded Rs 10 lakh from him.
As Tudu did not respond, he received an SMS which threatened him with dire consequences for not paying the money.
"We have already augmented security of the MP at his native place at Chandua, 15 KMs from here," Jena said, adding that a case under section 506 and 384 had been registered.