It said the Auditor-General's office and Comptroller-General's Department will head the probe if it goes ahead.
The threat came after the EC asked the Constitution Court if election re-runs should only happen in the 28 remaining constituencies, or whether a new royal decree should be issued to demand new polls be held nationwide.
The EC cited Section 108 of the constitution, which requires a general election to take place across the country on the same day. Polling did not take place in 28 constituencies in the South because anti-government protesters blocked registration of constituency candidates there.
Surapong Tovichakchaikul, caretaker deputy prime minister and chief adviser of the Centre for Maintaining Peace and Order (CMPO), said the EC would have to take responsibility if the election is declared void by the court.
Mr Surapong said he could ask the state auditor and the comptroller of public accounts to look into the EC's election spending to see if it was transparent. The commission could face multiple lawsuits for failing to perform its duty.
It not only failed to announce election results in constituencies where the election proceeded smoothly, but it could not organise the election in 28 constituencies in the South, he said.
The Pheu Thai Party is proposing the EC hold poll re-runs on March 30, the same day Senate elections will take place.
Party spokesman Prompong Nopparit said that if the EC agrees with the proposal, it should withdraw its petition with the court involving poll re-runs in the 28 southern constituencies.
Mr Prompong said anti-government demonstrators are unlikely to block the Senate election.
The proposal will be submitted to the EC when it meets tomorrow in Songkhla's Hat Yai district.
A group of 29 Pheu Thai Party candidates, earlier blocked from registering for the election, yesterday turned up at the EC's office. EC member Somchai Srisuthiyakorn asked the group to attend the meeting tomorrow.
Defending the EC's question of whether a decree should be issued for a new election nationwide, Mr Somchai said the court's ruling will offer a solution to the problem.
If the EC holds the poll re-runs in 28 constituencies, its critics would ask the court to rule whether this violates Section 108.