President Biden is hosting the leaders of Australia, India and Japan at his home in Wilmington, Del., this weekend, seeking to use his fourth and final “Quad summit” to cement the alliance between the United States and Indo-Pacific nations and to counter China’s rising influence in the region.

Mr. Biden will use the summit to expand both his “cancer moonshot” program and the Quad Fellowship, a scholarship program designed to build ties among the next generation of scientists and technologists. The four leaders will sign a maritime agreement and announce a joint Coast Guard mission.

There will be no specific policies aimed at China, according to Jake Sullivan, Mr. Biden’s national security adviser. But when Mr. Biden meets with Prime Minister Narendra Modi of India, Mr. Sullivan said, they will discuss how they see China’s actions in the region and where China is headed, and will work to try to coordinate approaches “to the extent that makes sense for both countries.”

Mr. Biden has often said that “all politics is personal,” and the decision to open his home in Wilmington — the first time he has invited foreign leaders there — reflected his conviction that deep relationships are the best way to forge constructive alliances. With just a few months left in the president’s term, this year’s summit will have a personal touch.

On Friday night, when the president had a one-on-one meeting with Prime Minister Anthony Albanese of Australia, he gave Mr. Albanese a tour of his home and told those in attendance to get comfortable and take off their jackets.

“The vibe of it was sort of two guys, one at the other guy’s home, talking in broad strokes about where they see the state of the world, you know, swapping some stories from their respective political careers,” Mr. Sullivan told reporters on Saturday. It felt, he said, as if “you had someone come over for a cup of coffee.”

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