When China’s top diplomat, Wang Yi, met with his Japanese and South Korean counterparts in Tokyo last weekend, he said China saw “great potential” for trade and stability if the three neighbors worked together. Citing what he called their shared “Oriental wisdom,” he quoted a proverb, seemingly alluding to the United States as an unreliable, distant ally: “Close neighbors are better than relatives far away.”

But even as the officials were talking, two Chinese Coast Guard ships had begun an unusual incursion into waters near disputed islands in the East China Sea. Japan’s coast guard, which moved to intercept them, said the Chinese ships were armed and had been pursuing a small Japanese fishing boat.

Japan said the incursion, which lasted nearly four days, was China’s longest yet into the waters around the islands, which are claimed by both countries. Japan’s foreign minister said he had protested to Mr. Wang on Saturday about an increase in such activity around the uninhabited islands, which Japan calls the Senkaku and China calls the Diaoyu.

China’s simultaneous pledges of friendship and deployment of armed ships reflect the two sides of Beijing’s strategy for dealing with a Trump administration that is rapidly recalibrating America’s place in the world.

China is using a “carrots and sticks” approach with its neighbors, to “reward the policies of the target country that advantage Chinese interests and warn against those policies that are harmful to China,” said Bonnie S. Glaser, the managing director of the Indo-Pacific Program at the German Marshall Fund, a Washington-based research institution.