NUUK, Greenland––The Pentagon raised an alarm last year over what it deemed a troubling development in this ice-cloaked territory: China was looking to bankroll and build three airports that could give it a military foothold off Canada’s coast.

Greenland’s prime minister had flown to Beijing in 2017 and asked Chinese state-run banks to finance the new commercial airports, including a big one for one of the smallest capitals on earth, Nuuk, which can now be served only by propeller planes. The bankers were interested, people...