Former Senator Kelly Ayotte, a Republican, entered the race for governor of New Hampshire on Monday, following Gov. Chris Sununu’s announcement last week that he would not run again for office in 2024.

“I’m running for governor because New Hampshire is one election away from becoming Massachusetts — from becoming something we are not,” Ms. Ayotte wrote in her campaign announcement. Maura Healey, a Democrat, flipped the Massachusetts governor’s office last year after Charlie Baker declined to run again. Both Mr. Baker and Mr. Sununu are popular moderate Republicans in their states.

Ms. Ayotte, a former attorney general in New Hampshire, was ousted from her Senate seat in 2016 by Maggie Hassan, a Democrat who had previously served as a popular governor of the state.

Ms. Ayotte’s candidacy for governor comes at a time when the state is receiving renewed attention from Republican presidential hopefuls, many of whom have repeatedly traveled to the state to court voters who will be among the first to go to the polls in the G.O.P. primary.

Ms. Ayotte is expected to garner widespread support among Republicans in the state, in a race that the nonpartisan Cook Political Report shifted to a tossup, from solid-Republican, after Mr. Sununu said he would not run again. Chuck Morse, the former president of New Hampshire’s state senate who lost the G.O.P. Senate primary against Ms. Hassan last year, entered the race almost immediately after Mr. Sununu’s announcement.

Two Democrats in the state — Cinde Warmington, a member of the New Hampshire Executive Council, and Joyce Craig, the mayor of Manchester — announced their candidacies ahead of Mr. Sununu’s declaration.

Ms. Ayotte faced a tough re-election campaign in 2016 even as Republicans gained power nationally. She served only one term in the Senate.

Though New Hampshire has had several recent statewide officials that are Republicans, the state has leaned blue during presidential elections, supporting Democrats in the last five.

Alongside her announcement, Ms. Ayotte rolled out a lengthy list of endorsements from dozens of Republicans across the state, who rallied around her candidacy.

But national Democrats were quick to criticize the former Senator and indicated that they plan to make abortion protections central in the race.

“Kelly Ayotte has spent her career working to stack the deck against New Hampshire’s working families and attacking their most fundamental freedoms — even leading the charge for a national abortion ban — which is why New Hampshire voters retired her seven years ago after a single term in the Senate,” wrote Izzi Levy, the deputy communications director for the Democratic Governors Association.

In her statement on Monday, Ms. Ayotte said she would seek to tackle crime by “standing up for our law enforcement officers” and would aim to “protect and strengthen New Hampshire’s economic advantage.”

She also signaled that she would lean into cultural issues motivating the Republican base, writing that she would “stand with parents, not bureaucrats, when it comes to deciding what is best for our children.”