(CBSDFW.COM) – After various county Republican parties in the state passed resolutions to censure Gov. Greg Abbott for the way he’s responded to the COVID-19 pandemic, Texas GOP Chairman James Dickey said Friday the state party could consider a censure resolution against him at the upcoming state convention.

Dickey said, “The next step would be submission of those to the platform and resolutions committee at the state convention.. The temporary committee will be getting their work on Monday. That is entirely up to the committee and then the body of the convention. There are several steps before any such thing would happen.. One of the reasons that we fight for conventions is because it is a bottom-up process where-in anything is possible within the rules, and within our structure. Anything is possible. If we’ve got grassroots folks who are fighting for it, that’s why we fight for our convention process.”

The Denton County Republican Party passed a censure resolution against the governor Thursday night.

The county parties have sharply criticized Abbott’s use of his executive authority, saying it goes against their party’s principles.

As cases of the virus and related hospitalizations have risen rapidly in Dallas and the state’s other large cities, the governor has issued a statewide order for people to wear masks in counties with 20 cases or more.

Two weeks ago, he ordered bars shut down and reduced capacity for in-dining occupancy from 75% to 50%.

Dickey said, “Well, I certainly understand why people are frustrated. This is an unprecedented time and we are all facing unprecedented challenges. There is a process in our party for handling these types of things. And that process has begun. The convention needs to be the next step in that this is all part of why it’s so important we move forward with our convention.”

Dickey, though, said as party chair, he is not taking an official position on the censure resolutions.

He said Republicans don’t squash dissent.

He is up for re-election as party chair against former Florida congressman and retired Army Lt. Col. Allen West.

The governor’s office didn’t respond to CBS 11 News’ request for comment, but Abbott has strongly defended his statewide order to wear masks to slow the spread of the virus as cases and hospitalizations have risen rapidly in Dallas and Tarrant counties along with the state’s other big cities.

In interviews late this week, the governor has said the next step after his order to wear masks would have to be a lockdown.

On Thursday, 11 state lawmakers who are members of the conservative Texas Freedom Caucus sent the governor a letter calling for reforming the Texas Disaster Act of 1975.

One idea mentioned in the letter includes limiting the time of the disaster declarations and allow the legislature to be called into a special session.

The Texas GOP is also battling the city of Houston after its in-person convention was canceled after Houston Mayor Sylvester Turner asked the operator of the George Brown Convention Center to review their contract with the party.

On Friday, the state GOP asked the Texas Supreme Court to allow them to hold their convention in Houston.

On Thursday, a Harris County judge rejected their request to do so.

Turner has said the in-person convention would put the public’s health at risk.

Dickey said the 5,000 attendees would have been able to properly socially distance in the large convention center and that the party was set to bring in thermal scanners to take the temperatures of people walking in.

Dickey accused the Mayor of playing politics. “So clearly, it was never about space. It was never about protection. It was never about social distancing. It was never about the state of the art thermal scanners that we had. It’s about a democrat politician wants to thwart the ability of Republicans to be able to vote and practice their political rights within his jurisdiction.”