The move came after local Internet users found that maps on the operating systems iOS 7 and version 10.9 of OS X ("Mavericks") automatically displayed "China Taiwan province" in simplified Chinese characters whenever they searched for "Taiwan" on the new iPhones.
"It does not fit with the reality," Kelly Hsieh, the head of the foreign ministry's Department of North American Affairs, told reporters.
"We've made representations to Apple Inc. Matters like this must not be compromised."
Bravo, a Taiwan PR company handling Apple Inc's media relations on the island, said the tech giant had no comment.
The name issue has been the subject of a highly contentious debate between Taiwan and mainland China since their split in 1949 at the end of a civil war.
Taiwan has styled itself as the "Republic of China", a name recognised by 23 countries, but is regarded by Beijing as part of mainland China waiting to be reunified by force if necessary.
Their ties have improved markedly since Ma Ying-jeou of the current Beijing-friendly government took office in 2008 with a promise to beef up trade and tourism links. Ma was re-elected in January 2012.