Mr Supachai was speaking while inspecting the central advance voting unit in Nonthaburi province on Sunday morning.
The voting, which began at 8am throughout the country, will continue until 3pm.
He said so far there had not been reports of any moves to obstruct the voting and believed Sunday's poll would continue smoothly without disruption.
On the National Anti-Corruption Commission's ruling that Nikom Wairatpanich had breached the constitution for his role in chairing parliamentary meetings that were considering a charter amendment bill on the composition of the Senate, resulting in him being suspended as Senate speaker, Mr Supachai said this would not be a problem since a deputy Senate speaker can perform the duty on his behalf.
If there are no problems, the result of the Senate election to be held on Mar 30 was expected to be announced within seven days, he said.