Mr Varathep was responding to the EC's call for caretaker Prime Minister Yingluck Shinawatra to arrange a meeting to discuss deferring the election.
He reiterated that the government did not have the authority to postpone the poll date.
If the EC wanted to press ahead with its idea to seek a Constitution Court interpretation on the actual scope of the caretaker government's power regarding an election postponement, the administration would have no comment, Mr Varathep said.
Mr Varathep said all he could say was that the EC should carry on with its task of organising the election.
Over the past few weeks, the government had resolved two major obstacles and the rest of the procedures should be completed by the EC, he said.
Mr Varathep said the government had solved the shortage of state officers to take care of the polling stations and had assigned the National Police Office, the Interior Ministry and the Education Ministry to ensure security for the EC.
It was the EC's responsibility to deal with the 28 constituencies where no candidate could register for the election.
As it stands, not enough constituents would be elected to formalise the first House session after the election.
Mr Varathep said he was not worried about the role of the EC or the National Anti-Corruption Commission, even though they appear to be putting a lot of pressure on the government.
Society understood what was happening and could decide who was right and who was wrong, he said.
The government has taken a firm stance that reform has to be conducted along with the election, as it would be impossible to agree to changes in the short time available before the poll.
Mr Varathep said in the week ahead the parties taking part in the poll would announce an agreement to start reform after the election.