The Trump administration’s efforts to extradite the chief financial officer of China’s Huawei Technologies Co. over criminal charges mark the start of an even more aggressive phase in the technology rivalry between the U.S. and China and will increase pressure on Washington’s allies to shun the telecommunications company.

Armed with a U.S. extradition request, Canadian authorities arrested Meng Wanzhou on Dec. 1, the same day as President Trump was holding a summit with Chinese counterpart President Xi Jinping. But White House...