US counterterrorism officials disputed his claim that the sons were captured and a White House official said: "We, in fact, think it's wrong."
Sanaullah Zehri, who as home minister of Pakistan's Baluchistan province is the area's top security official, said the raid was carried out by "allied forces" including US troops in an area of Afghanistan where the borders of Iran, Pakistan and Afghanistan converge.
Mr Zehri said the sons captured were Saad and Hamza bin Laden.
At the Pentagon, two senior officials said they could not confirm that sons of bin Laden had been arrested. They said they did not know if the report was correct, but that there was no indication of US military involvement in such an operation.
Mr Zehri's claim was not confirmed by other Pakistani officials. The interior ministry, information ministry, and frontier constabulary a paramilitary force along the border all said they could not independently confirm the report.
Afghanistan's Interior Ministry spokesman Mohammed Daoud said he was unaware of the arrests. "We have no information on this," he said in the Afghan capital of Kabul.
Saad, believed to be aged 23 years and bin Laden's eldest son, is also on the American most-wanted list and has been said to be a rising star in the terror network.
The al-Qaida leader is believed to have up to 23 sons by several wives.
"They were arrested from Rabat area in Afghanistan," Mr Zehri said from his home in Quetta, the Baluchistan provincial capital. Rabat is in the extreme south-west of Afghanistan's Nimroz province.
He said that eight suspected al-Qaida men had also been injured in the assault in Rabat. They had been taken to the Rabat hospital and among them were two of bin Laden's sons, he said.
"This is what my information is. This is what I have been told, but our soldiers were not involved. There were no Pakistanis involved. I am getting my information from my sources and this is what I have heard," Mr Zehri said. He would not say how he got the information or whether he had been able to verify it himself.
The reported capture of bin Laden's sons came within a week of the arrest in Pakistan of Khalid Shaikh Mohammed.
Mohammed, the number three al-Qaida leader and suspected mastermind of the September 11 attacks, was caught during a raid near Islamabad on Saturday.
He has reportedly told his interrogators that bin Laden is alive and well and living in the lawless border area between Pakistan and Afghanistan.
And he said he had met the terrorist leader just weeks ago in Pakistan's Baluchistan province after arranging a rendezvous through a complicated network of phone calls, runners and intermediaries.