The Afghan Taliban told Al Jazeera said they had no need for the help of Pakistani fighters and do not recognise their leadership.
The Pakistani army has been conducting a campaign against the Taliban in that region for several months and the offensive is believed to have pushed many of Taliban fighters in the area to flee.
There are thought to be as many as 10,000 fighters in South Waziristan, including hundreds of Uzbek fighters.
The Pakistani military estimates it has killed about 600 Taliban fighters, but in his interview Rehman claimed to have lost fewer than 20 men.
"We have not noticed any significant movement of insurgents in the border area"
Colonel Wayne Shanks,
US military spokesman in Afghanistan
Imran Khan, Al Jazeera's correspondent in Islamabad, said Rehman's interview was likely an attempt to play down the effects of the military's offensive in South Waziristan.
"They're saying here that the Taliban is putting a spin on it - it's a confident performance, but they've been forced into Afghanistan by the offensive [in South Waziristan]," he said.
"This is the Taliban saying we've not been forced by the Pakistani army, we're going across voluntarily."
The Associated Press interview with Rehman was conducted at a mud-brick compound in the Shaktoi area of South Waziristan on Monday.
The news agency also quoted Colonel Wayne Shanks, a US military spokesman in Afghanistan, as dismissing Rehman's comments as simply "rhetoric".
"We have not noticed any significant movement of insurgents in the border area," he said.
Imtiaz Gul, an expert on the Pakistani Taliban, said that Rehman's comment's needed to be taken "with a pinch of salt".
"If we look at the track record of the Tehreek-e-Taliban Pakistan [the Pakistani Taliban, or TTP], they have been exclusively concentrating on targeting Pakistani army, Pakistani people and government installations," he told Al Jazeera.
"If Walid Rehman Mehsud has made this claim, this indicates perhaps a change in tactic or an attempt to divert attention from the TTP.
"Especially after the sweeping operation the army has conducted, they probably want to send a reassuring signal to their supporters that they are very much alive and kicking."
In his interview Rehman also said his group would stop attacking Pakistani forces if Pakistan would sever its ties to the US.
"We would again become Pakistan's brother if Pakistan ends its support for America," he was quoted as saying.
He urged the US president to focus on concerns at home, saying: "He should know that Americans don't want war ... He should use this money for the welfare of his own people."