SALEM, Ore. — In a typical month, 2,000 people register to vote in Oregon. In the first six days of this year, more than 4,300 joined the voter rolls under a new initiative that automatically signs up voters when they apply for driver’s licenses.

Oregon is the first state to adopt the idea that it is the government’s responsibility to register voters — a move that could increase the number of registered voters by 13 percent by the November election.

California has approved similar legislation, and automatic registration bills have been introduced in more than a dozen other states. “There’s no other fundamental right we have as citizens that requires you to register or fill out a form,” said Alex Padilla, California’s Democratic secretary of state, who advocated for the law. “I don’t have to register somewhere to exercise my freedom of speech. I don’t have to fill out a form somewhere to exercise my right to not be discriminated against.”

Researchers at the Pew Center on the States reported in 2012, before the last presidential election, that 51 million Americans were eligible to vote but unregistered. Pew said last year that the United States has one of the lowest voter-participation rates of the democratic world.

President Barack Obama praised Oregon and California twice last month and urged more states to follow their lead.

“The job of our democracy is to make it easier, not make it harder for our citizens to be able to vote,” Obama told Democratic governors on Feb. 19.