Gov. Katie Hobbs of Arizona vetoed a bill on Monday that would have authorized the state police to arrest undocumented immigrants.

It was the first veto of the year from Ms. Hobbs, a Democrat who shot down a record number of bills passed by Arizona’s Republican-controlled Legislature in 2023 dealing with abortion, elections, L.G.B.T.Q. rights and other hot-button issues.

Her veto highlights the election-year tensions over border security as border states and major cities grapple with a record number of migrants crossing the southern border. Ms. Hobbs has expressed frustration with the Biden administration’s handling of the border crisis, but said the Republican-backed measure was anti-immigrant and most likely unconstitutional.

The bill, called the Arizona Border Invasion Act, would have made crossing the border without authorization a misdemeanor state crime, and a felony for migrants who crossed after being deported or ordered to leave. It would also have allowed state law enforcement officials to detain migrants, and Arizona judges to order deportations.

Ms. Hobbs said that the measure “does not secure our border, will be harmful for communities and businesses in our state and burdensome for law enforcement.” She also said that it potentially violated the U.S. Constitution by claiming what has long been the federal government’s exclusive power to arrest and deport immigrants.

The bill echoed a new Texas law — now blocked in court — that has set off a legal confrontation between the Biden administration and Texas officials over whether the state can enforce immigration policy. On Monday, the Supreme Court signaled it would intervene in the battle between Texas and the Biden administration.