Republicans and Democrats in Texas are locking horns over coronavirus-related efforts to expand voting by mail, with Republicans arguing it can fuel voter fraud and Democrats warning that disallowing it could harm turnout and sway results.

The Texas Democratic Party has filed two lawsuits against state election officials and Republican Gov. Greg Abbott to extend the state’s limited mail-in eligibility. A state district judge Wednesday afternoon said he would grant Democrats an injunction to allow Texans to vote by mail; state...