WASHINGTON — Emboldened House Democrats, seeking a politically charged debate on gun control, unveiled legislation on Tuesday to expand background checks to nearly all firearms purchases, a move timed to mark the eighth anniversary of the mass shooting in Arizona that nearly killed former Representative Gabrielle Giffords.

By introducing the measure less than one week after taking control of the House, Democrats are signaling that it is a top priority. A vote could come within the first 100 days of the new Congress. The measure, and a companion bill introduced Tuesday in the Senate, also reflects the changing politics around gun laws, an issue many Democrats once shied away from.

The bill, which will almost certainly pass the House but will face a steep climb in the Republican-controlled Senate, would require background checks on the purchases of nearly all firearms, including those sold at gun shows and over the internet. There would be limited exceptions, including for law enforcement officers and for guns transferred between close family members.

Polls have shown that a vast majority of Americans — by some estimates, 90 percent — support universal background checks for all gun purchases. Many Democrats, including Representative Lucy McBath, a freshman from Georgia whose son was shot and killed at a Florida gas station, were elected last year after promising to address gun safety.