China is moving swiftly to capitalize in Asia on the apparent collapse of a landmark U.S.-backed Pacific trade agreement, saying it hopes now to conclude its own Asia-wide trade pact in a step to broaden its influence as priorities shift under a new administration in Washington.

Asian leaders are pressing ahead with talks on the 16-nation Regional Comprehensive Economic Partnership, which China has promoted as an alternative to the U.S.-led Trans-Pacific Partnership.

Leaders...