Four of South Dakota’s federally recognized Native American tribes have barred the state’s governor, Kristi Noem — a Republican whose name has been floated as a potential running mate for former President Donald J. Trump — from their reservations. The latest blocked Ms. Noem on Thursday.

Three of the tribes barred Ms. Noem this month, joining another tribe that had sanctioned the governor after she told state lawmakers in February that Mexican drug cartels had a foothold on their reservations and were committing murders there.

Ms. Noem further angered the tribes with remarks she made at a town hall event last month in Winner, S.D., appearing to suggest that the tribes were complicit in the cartels’ presence on their reservations.

“We’ve got some tribal leaders that I believe are personally benefiting from the cartels being there, and that’s why they attack me every day,” Ms. Noem said.

The tribes are the Cheyenne River Sioux, the Rosebud Sioux and the Standing Rock Sioux and the Oglala Sioux, which in February became the first group to bar Ms. Noem from its reservation. Their reservations have a combined population of nearly 50,000 people and encompass more than eight million acres, according to state and federal government counts. Standing Rock Indian Reservation, the third tribal area to have restricted Ms. Noem’s access, extends into North Dakota.

The tribes have accused Ms. Noem of stoking fears and denigrating their heritage when she referred to a gang known as the Ghost Dancers while addressing state lawmakers and said that it had recruited tribal members to join its criminal activities.

The gang has the same name as the participants in the Native American ghost dance ceremony, a sacred ritual dating to the 19th century.

“Gov. Kristi Noem’s wild and irresponsible attempt to connect tribal leaders and parents with Mexican drug cartels is a sad reflection of her fear-based politics that do nothing to bring people together to solve problems,” Janet Alkire, the chairwoman of the Standing Rock Sioux Tribe, said in a statement this week.

Ms. Noem stood by her comments in a statement to The New York Times on Friday.

“Tribal leaders should immediately banish the Mexican drug cartels that are responsible for murders, rapes, drug addiction and many more crimes on tribal lands,” she said. “The people in the communities live with unspeakable horrors and tragedy every day, but banishing me for telling the truth about the suffering does nothing to solve the problems. It may play well for the leftist media, but in reality, it’s pointless.”

When asked about Ms. Noem’s claims that tribal leaders were benefiting from the cartels’ presence on reservations, an aide pointed to her recent remarks to The Dakota Scout, an alternative newspaper based in Sioux Falls, S.D., doubling down on them and criticizing the tribes’ response to the cartels.

“That tells me that they are tied to them or benefiting from them somehow, that they’re allowing them to stay in their communities,” she said.

The governor’s office provided photos to The Times that it said were from a gang promotion ceremony featuring several men wearing clothing adorned with Ghost Dancers patches. The Times was unable to verify the images independently.

It also released a recording of a conversation that it said was between the secretary of the South Dakota Department of Tribal Relations and a leader of the Standing Rock Sioux Tribe in which they discussed how a single Tribal Council representative from South Dakota had voted to bar Ms. Noem from its reservation. The remaining votes came from Tribal Council members who reside in North Dakota, according to the governor’s office.

Efforts to reach the Tribal Council member said to be in the recording were not immediately successful.

In a social media post on Thursday, Ms. Noem argued that her comments about cartel activity on the reservations were similar to remarks that Senator Jon Tester, Democrat of Montana, made last month before the Senate Indian Affairs Committee.

“We’ve got cartels in Indian Country,” he said, using an expletive to say there was a lot of “bad” stuff going on.

Mr. Tester, a member of the Indian Affairs Committee, had been pushing for additional law enforcement resources for tribal lands, mirroring calls from tribal leaders in Montana for help from the federal government in addressing crime. His comments differed in tenor from Ms. Noem’s, and he did not level accusations that tribal leaders were complicit in the rise of the cartels on reservations.

A spokesman for Mr. Tester, who is running for re-election in a crucial contest for control of the Senate, declined to comment on Friday.

In November, the Oglala Sioux Tribe, citing a rise in drug-related offenses, assaults and homicides on its reservation, declared a state of emergency, which remains in effect.

Then, in January, the tribe accused the federal government in a lawsuit of failing to provide adequate funding as required by longstanding treaties for law enforcement coverage on the reservation, an area larger than Rhode Island and Delaware combined.

The tribe said in its lawsuit that it receives enough federal funding for only 33 police officers and eight criminal investigators, which it said had contributed to an uptick in crime. But the tribe pushed back against Ms. Noem’s claims that the cartels were using the reservation to facilitate the spread of illegal drugs and said that the problem existed when Mr. Trump was president.

The cartels’ reach on tribal lands is gaining heightened attention on Capitol Hill, where at least two congressional panels recently focused on surging crime connected to the groups.

At a hearing on Wednesday, Jeffrey Stiffarm, a tribal leader from Montana, told a House oversight committee that “these drug cartels are specifically targeting Indian Country because of a dangerous combination of rural terrain, history of addiction, under-resourced law enforcement, legal loopholes, sparsely populated communities and exorbitant profits, and it is devastating tribal reservations.”

South Dakota has nine federally recognized Native American tribes, which have at times sparred with Ms. Noem over issues related to their sovereignty, her support for the now-halted Keystone XL pipeline and access to their reservations at the start of the coronavirus pandemic.

The president of the Oglala Sioux Tribe, which in 2019 lifted a previous barring of her, said the governor’s political ambitions had motivated her actions.

In a statement posted on Facebook in February, the president, Frank Star Comes Out, said that “the truth of the matter is that Governor Noem wants the use of the so-called ‘invasion’ of the southern border as a Republican ‘crisis’ issue” to encourage Mr. Trump to use it as a campaign issue and to select her as his running mate.

At the Conservative Political Action Conference later in February, a straw poll showed Ms. Noem tied for the top choice to be Mr. Trump’s running mate.

The tribes’ criticism of Ms. Noem began after the governor addressed a joint session of the South Dakota Legislature on Feb. 2 about the tide of illegal border crossings.

“Make no mistake, the cartels have a presence on several of South Dakota’s tribal reservations,” she said. “Murders are being committed by cartel members on the Pine Ridge Reservation and in Rapid City, and a gang called the Ghost Dancers are affiliated with these cartels. They have been successful in recruiting tribal members to join their criminal activity.”

Ms. Noem said the state government did not have the jurisdiction to intervene and provide law enforcement support to South Dakota’s tribes.

On Thursday, Ms. Noem announced that South Dakota would begin offering training to tribal law enforcement officers, who currently must travel to New Mexico for it.

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