Turner was joined by leaders including Harris County Judge Lina Hidalgo and Fort Bend County Judge K.P. George at the George R. Brown Convention Center on Monday.
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Multiple major corporations based in Texas have already spoken out in opposition to Republican-led legislative proposals to further restrict voting in Texas.
SEE RELATED: 2 big Texas companies come out against GOP bills to tighten voting laws
Corporate giant American Airlines took specific aim at Senate Bill 7, which would impose sweeping restrictions that take particular aim at local efforts meant to make it easier to vote - like extended early voting hours. Senate Republicans advanced that measure in a vote last week.
Another voting proposal that's caused controversy is House Bill 6, which prohibits local election officials from proactively sending out applications for mail-in ballots and impose new rules for people assisting voters to fill out their ballots.
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SEE RELATED: New GOP-led voting restrictions move forward in Texas
Both measures are legislative priorities for Texas Republicans, who this year are mounting a broad campaign to scale up the state's already restrictive voting rules and pull back on local voting initiatives championed in diverse urban centers, namely in Harris County, during a high-turnout election in which Democrats continued to drive up their margins. That push echoes national legislative efforts by Republicans to change voting rules after voters of color helped flip key states to Democratic control.
The Texas Tribune contributed to this report.