Ahmad Garavand, deputy border police chief, told reporters his forces had arrested a US woman "spy" at the town of Jolfa on the border with Azerbaijan, Fars news agency reported.
He identified the woman as Hal Talayan, 34.
"This American woman spy has been arrested at Jolfa" in northwestern Iran, Garavand was quoted as saying.
"According to the border control intelligence bureau this person was arrested on January 5 while she was filming under cover as a tourist, and she was on a mission from the US spy agency," he said.
On Thursday, Fars news agency reported that Talayan had been arrested last week on the border with Armenia.
Later, however, Iran's Al-Alam television cited a security source as saying a US woman had been refused entry at a border crossing with Armenia a week ago over a visa problem.
"She approached the border guards, but as she did not have a visa, she was not authorised to enter Iran. She was sent back to Armenia," the television station said.
But Armenia denied on Friday that the woman had ever been to the former Soviet republic, and the United States said it had no information to confirm that Iran had detained an American citizen on spying charges.
"We have no information to corroborate this alleged incident," State Department spokesman Philip Crowley said on Friday.
In a separate report on Saturday, ISNA quoted Garavand as saying the detainee was "tasked by Americans to film the borders."
She "was filming the border markets, Jolfa (police) station and the frontier," Garavand said.
"She was arrested at Jolfa border and handed over to the intelligence bureau," he said, adding that the woman was carrying "advanced filming equipment" and that the issue was now under further investigation.
Talayan would be the fourth American to be arrested by Iran on spying charges along with hikers Sarah Shourd, Shane Bauer and Josh Fattal.
The three insist they innocently strayed across the border when they were detained on July 31, 2009 during a hike in the Iraqi Kurdistan region.
While Shourd was released last year on humanitarian grounds, Iranian authorities have not dropped the case against her and officials have set February 6 as a trial date for all three hikers.
That is close to the anniversary of the 1979 Islamic revolution and the fall of the US-backed shah's regime - when anti-American rhetoric traditionally reaches a climax in Iran.
After Shourd was freed on hefty bail in September, President Mahmoud Ahmadinejad suggested that the United States free eight jailed Iranians as a "humanitarian gesture" in exchange for the two remaining hikers.
US State Department spokesman Mark Toner rejected any link at the time.
"We would just say that there is no equivalent between these individuals who have been either charged or tried and afforded due process in a court and these hikers who crossed an unmarked border and have yet to be charged," Toner said.
The animosity between Iran and the United States has grown with Tehran under mounting international pressure led by Washington over its controversial nuclear programme which the West suspects of covering a weapons drive.
Iran denies the charge and is due to hold a second round of talks over its nuclear programme with world powers in Istanbul in late January.
Iran is also detaining two German journalists after they were arrested in October while interviewing the son of a woman condemned to death by stoning.
Tehran says the Germans entered the country on tourist visas and failed to obtain the necessary accreditation for journalists before "posing as reporters" when they contacted Sakineh Mohammadi Ashtiani's family.