David Olivier, 31, and Widmar Daniela, 29, were abducted by gunmen in the Loralai area of southwestern Balochistan province in July.
They had entered Balochistan as tourists but officials said that they had not informed the authorities of their arrival.
The Tehrik-i-Taliban Pakistan (TTP) has released the videos which were shown by Dawn television Wednesday.
Three armed men are standing behind the couple in the video, reported Xinhua.
Dawn TV said that the couple are being held hostage by the TTP in North Waziristan tribal region.
The videos show the couple calling upon the governments of Switzerland, the US and Pakistan to meet the captors' demands.
The TTP said they would release the couple if the US freed Aafia Siddiqui, a female neuroscientist sentenced in 2010 for attack on US soldiers in Afghanistan.
"We call upon the Western world to put pressure on America for the release of Aafia Siddiqui," TTP deputy chief Waliur Rehman said.
"If the US does not agree to her release then our central 'Shura' (council) will take a decision about the Swiss hostages," he added.
In one video, one of the hostages said "our lives are at risk" if the demands are not met.
Sources said that the TTP members had delivered the videos to local journalists in Miranshah in North Waziristan.