Some prominent local politicians, such as Jones and state Senator Brooks McCabe, D-Kanawha, have stated the amendment is an effort to prevent gay marriages from occurring.
Jones also claims the issue was brought up in a Republican caucus in the House.
"It came up in the Government Organization Committee that Charleston wanted to do gay marriage," Jones said.
That's another allegation Armstead hotly denies.
"Some individual delegates may have discussed gay marriage, but it was never brought up in any of the caucuses," he said.
Armstead pointed out that the bill was amended to include the provision about marriage in the House of Delegates Government Organization Committee before it came to the House floor.
Delegate Jim Morgan, a Democrat from Cabell County, is chairman of the Government Organization Committee.
The bill was also amended on the House floor. This amendment required all cities participating in the home rule program to drop any and all gun ordinances.
Jones pointed out that he couldn't legally perform gay marriages, even if he were granted the power to preside over a wedding by the state.
"I can't make gay marriage legal," Jones said. "Gay marriages will either be legal, or illegal, depending on the (U.S.) Supreme Court."
He is unsure if he will continue to pursue the power to perform marriages or attempt to have his ministry validated by the secretary of state.
"I probably won't," he said. "But I do have a lot of people ask me to marry them.
"They think I already have the power to do it," Jones added.
Jones' speech to council where he made the statements about Armstead and the House of Delegates is on YouTube.
Armstead believes Jones' recent outspoken criticism of the Legislature hurts Charleston moving forward.
Jones has also strongly criticized the House of Delegates' amendment to the home rule bill nullifying Charleston's gun ordinance.
Charleston, which is one of four home rule cities currently in the state, has ordinances requiring a three-day waiting period for the purchase of a handgun and background checks for the purchase of a handgun.
The city also restricts individuals to one handgun purchase every 30 days.
"He can say what he wants, but the way this has played out could make it more difficult for Charleston to get legislative support for anything in the House," Armstead said.