"It's not their job to send a warning letter; it is completely wrong," U Tin Oo told Mizzima.
"The accusation has no basis in law," he said.
U Tin Oo was referring to a warning letter sent by the UEC to Daw Aung San Suu Kyi on May 22 over a challenge she issued to Tatmadaw MPs to support constitutional change.
The letter warned the NLD leader, who issued the challenge in a speech in Mandalay on May 18, that Tatmadaw MPs were sitting in parliament under the provisions of the 2008 Constitution and her use of the word "challenge" was unacceptable.
The letter quoted Daw Aung San Suu Kyi as having said: “I would like to suggest that you prove you are not doing this for authority, power and special opportunities. The word ‘suggest’ here is more like a challenge. I want to challenge you.”
The NLD has said Section 345 of the constitution provides for citizens to freely express an opinion.
Ko Ko Gyi of the 88 Generation Peace and Open Society movement, which is campaigning with the NLD for constitutional reform, said the UEC had sent the letter "because it is overwhelmed by fear".
Ko Ko Gyi said Daw Aung San Suu Kyi's intention in making the comment was to raise the dignity of the Tatmadaw.
"The election commission should not have issued the warning at all," he said.