TALLAHASSEE (CBSMiami/NSF) – Florida’s texting-while-driving ban would be strengthened under a proposal filed by Sen. Thad Altman for the 2016 legislative session.

The measure would make texting while driving a “primary” offense — meaning police could pull over motorists who violate the ban.

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Under current law, it is considered a “secondary” offense. That means motorists can only be cited for texting while driving if they are stopped for other reasons.

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Past attempts to make texting while driving a primary offense have failed.

Altman’s measure goes further than a bill filed in August by Rep. Richard Stark that would toughen penalties for motorists who text while driving in school zones or at school crossings. Stark’s bill calls for doubling fines for motorists who violate the texting-while-driving ban in the designated school areas.

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The News Service of Florida contributed to this report.