President Trump, seeking to counter China’s growing geopolitical influence, is embracing a major expansion of foreign aid that will bankroll infrastructure projects in Africa, Asia and the Americas — throwing his support behind an initiative he once sought to scuttle.

With little fanfare, Mr. Trump signed a bill a little over a week ago that created a new foreign aid agency — the United States International Development Finance Corporation — and gave it authority to provide $60 billion in loans, loan guarantees and insurance to companies willing to do business in developing nations.