BEIJING/TAIPEI (Reuters) - China will strike back against any moves that undermine its core interests, its foreign ministry said on Friday, after U.S. Secretary of State Mike Pompeo said that Taiwan “has not been a part of China”.China calls Taiwan the most sensitive and important issue in its ties with the United States, and has been angered by the Trump administration’s stepped up support for the Chinese-claimed yet democratically ruled island, such as arms sales. Speaking in a U.S. radio interview on Thursday, Pompeo said: “Taiwan has not been a part of China”. “That was recognised with the work that the Reagan administration did to lay out the policies that the United States has adhered to now for three-and-a-half decades,” he said. The United States is bound by law to provide Taiwan with the means to defend itself, and officially only acknowledges the Chinese position that Taiwan is part of it, rather than explicitly recognising China’s claims. Speaking in Beijing, Chinese foreign ministry spokesman Wang Wenbin said Taiwan was an inalienable part of China and that Pompeo was further damaging Sino-U.S. ties. “We solemnly tell Pompeo and his ilk, that any behaviour that undermines China’s core interests and interferes with China’s domestic affairs will be met with a resolute counterattack by China,” he said, without elaborating. China has put sanctions on U.S. companies selling weapons to Taiwan, and flew fighter jets near the island when senior U.S. officials visited Taipei this year. The defeated Republic of China government fled to Taiwan in 1949 after loosing a civil war to the communists, who founded the People’s Republic of China.