"According to some US individuals, including the group State Department Watch, eight Arctic islands currently controlled by Russia, including Wrangel Island, are claimed by the United States. However, according to the United States Department of State no such claim exists." - link
On an off-topic but related note, the US also has mostly exclusive claims over a number of Pacific Islands, some of which have been shown not to exist, or at least, not to exist any longer. Vincent Gaddis, writing in “Strange” magazine about 15 years ago, penned a fascinating article about various vanished and intermittent islands.