Arizona voters will decide in November whether to establish a right to abortion in the state constitution, a measure that could strongly influence turnout in a battleground state that is critical to the presidential election as well as control of the Senate.

The Secretary of State’s office said it had certified 577,971 signatures that abortion rights groups had collected over the last months, 50 percent more than were required to put the constitutional amendment on the ballot in November and the highest number of certified signatures for any ballot measure in state history.

In the two years since the Supreme Court overturned Roe v. Wade, which had established a right to abortion in the United States Constitution, abortion rights groups have prevailed in all seven states where the question of abortion has been put directly before voters. Anti-abortion groups, which had sponsored almost all abortion-related ballot measures before Roe was overturned, have been pushed onto defense, running “decline to sign” campaigns and filing lawsuits trying to prevent signatures from being certified.

Similar measures on abortion rights are already on the November ballot in six other states, but only two are battleground states — Arizona and Nevada. (The others are Florida, South Dakota, Colorado, New York and Maryland.) And Democrats are hoping that support for abortion rights will drive higher turnout in their favor.

Democrats have leveraged unhappiness over Roe’s demise into gains in elections up and down the ballot over the last two years. More young women in particular have shifted toward the party, a demographic that Democrats hope will prove critical in November, and the party’s nominee, Vice President Kamala Harris, has campaigned energetically on her support for abortion rights.

Arizona is critical in the fight over control of the U.S. Senate. Ruben Gallego, a Democratic representative, is facing off against Kari Lake, the Republican nominee, for an open seat.