Media reports have identified the men as charity medic Kevin Cornwell, 53, the unnamed manager of a hotel for aid workers and YouTube star Miles Routledge.
“The government is in negotiations and working hard to ensure people’s safety is upheld,” Braverman told Sky News.
The non-profit group the Presidium Network said on Twitter on Saturday it had been “working closely with two of the families”.
“We are working hard to secure consular contact with British nationals detained in Afghanistan and we are supporting families,” the UK’s foreign ministry added in a statement.
Scott Richards of the Presidium Network told Sky News: “We believe they are in good health and being well treated.
“We have no reason to believe they’ve been subject to any negative treatment such as torture and we’re told that they are as good as can be expected in such circumstances.”
He added, however, that there had been “no meaningful contact” between authorities and the two men Presidium was assisting.
These two men are believed to have been held by the Taliban since January.
It is not known how long the third man has been held for.
Presidium on Twitter urged the Taliban to be “considerate of what we believe is a misunderstanding and release these men”.
Last year the Taliban freed a veteran television cameraman and four other British nationals it had held for six months.
Peter Jouvenal was one of a “number” of Britons that the government in London said had been held by the hardline Islamists.
Britain’s foreign ministry said the five “had no role in the UK government’s work in Afghanistan and travelled to Afghanistan against the UK government’s travel advice.”
“This was a mistake,” it added.
At the time, Afghanistan government spokesman Zabihullah Mujahid accused the Britons of “carrying out activities against the country’s laws and traditions of the people of Afghanistan”.
“After consecutive meetings between the IEA (Islamic Emirate of Afghanistan) and Britain the said persons were released… and handed over to their home country,” he said.
“They promised to abide by the laws of Afghanistan, its traditions and culture of the people and not to violate them again,” he added.
The Taliban returned to power in August 2021 and has since sparked global outrage with its policies in particular towards women and girls.