An Arizona man who allegedly vowed to assassinate Donald Trump has been apprehended by police after going on a manhunt while the former president was in the border state.

Ronald Lee Syvrud, 66, of Cochise County, is accused by police of threatening to kill President Trump on social media during the previous two weeks.

Trump visited the US-Mexico border on Thursday while in Cochise County.

During a campaign rally in Butler, Pennsylvania, last month, Trump was slightly injured by a gunshot during an attempted assassination.

The Cochise County Sheriff’s Office says Syrvud is also wanted for failing to register as a sex offender.

He faces several warrants in both Wisconsin and Arizona, including on charges of driving under the influence and a felony hit and run.

Police say he is from Benson, Arizona, which is located about 50 miles (80km) south-east of Tucson.

The Cochise County Sheriff's Office posted on Thursday afternoon that they had caught the suspect within the county lines.

"This subject has been taken into custody without incident," the office posted.

Trump spent Thursday in Cochise County, visiting the US-Mexico border.

During his remarks, he sought to blame his rival, Democratic presidential nominee Kamala Harris, for allowing illegal immigrants into the US.

Reporters asked him if he was aware of the search for the Cochise County suspect.

"No, I have not heard that but I am not that surprised and the reason is because I want to do things that are very bad for the bad guys," Trump said.

This isn't the first threat against a presidential candidate this election cycle.

Earlier this month, a 66-year-old Virginia man was arrested on suspicion of making death threats against Vice-President Harris, among other public officials.