Attorney General Ken Paxton of Texas went to court on Wednesday to try to stop county leaders in San Antonio from sending out more than 200,000 voter registration applications to unregistered residents of Bexar County.

The lawsuit by Mr. Paxton followed a letter he sent days earlier warning Bexar County officials, most of whom are Democrats, against proceeding with the mailing. The county’s governing commissioners voted 3 to 1 on Tuesday to approve the proposal anyway.

Mr. Paxton has also threated to sue Harris County, which includes the Democratic stronghold of Houston, where officials have been weighing a similar effort to expand the number of registered voters ahead of the registration deadline early next month for the November election.

The suit is the latest chapter in a yearslong conflict over voting and elections in Texas between Republicans, who dominate state government, and Democrats, who control most of the state’s largest urban areas.

Across the country, there have been other fights over registration, including in Michigan, where the Donald J. Trump campaign is trying to stop a state effort to expand registration at federal offices. Nine Republican state attorneys general sued the Biden administration last month over a three-year-old executive order directing the federal government to expand registration, a suit that also included other Republican opponents of the order.

In Texas, state officials have become increasingly aggressive in recent weeks in their attempts to prevent what Mr. Paxton has said are efforts to circumvent the state’s strict election rules in ways that could lead to fraud in the November election.