"We now have to agree on the legal framework between SBB and Apple," SBB spokesman Reto Kormann said, adding that Swiss railways still held the trademark for the emblematic clock designed by Zurich-born engineer Hans Hilfiker in 1944.
"SBB isn't hurt, but proud that his icon of watch design is being used by a globally active and successful business."
Mondaine Group, the company that has held the licence since 1986 to make clocks and wristwatches for consumers based on the 20th-century design classic, said it would also challenge Apple.
"The app is pretty much identical to our Mondaine watch," Andre Bernheim, the company's co-owner, told Reuters. "Three companies together - Apple, SBB and Mondaine - can together achieve something positive. We'll see how this all ends up."
An Apple spokesman was not immediately available to comment.
The minimalist clock, which is emblematic of Switzerland's tradition of punctuality, was designed for the national rail service to help travellers to check the time at a distance as they hurried to catch their trains.
In 1953 Hilfiker added a red second hand, which pauses briefly at the top of each minute "to enable trains to depart punctually", as he put it.
The second hand with a circle at its end is based on the device a station manager on the platform would wave for a train's departure, and SBB holds the rights to the design.
"Yet again we see that something that looks simple isn't simple," Bernheim.
The redesigned clock app is a new feature on Apple's iPad computer with the iOS 6 mobile operating system. It uses black dashes for numbers and a red second hand with a circle at the end, just like the Swiss railway clock, a Reuters employee visiting an Apple store observed.
The Museum of Modern Art in New York and the Design Museum in London have both included Hilfiker's clock among their examples of outstanding 20th-century design.
Switzerland's tradition of watchmaking stretches back hundreds of years and includes famous luxury watchmakers such as Patek Philippe, Rolex and Omega.
(Reporting by Catherine Bosley; Editing by David Goodman)