BEIJING — President Xi Jinping of China spoke by phone on Wednesday with the president of the Philippines, Rodrigo Duterte, in what Chinese news media described as a friendly call that came just a few days after President Trump’s amicable conversation with the authoritarian Filipino leader.

Mr. Xi’s outreach to Mr. Duterte appeared to be part of efforts by the Chinese to woo a longtime American ally and strengthen their sovereignty claims in the South China Sea.

Chinese news media said North Korea and other issues were discussed in the phone call. On Saturday, Mr. Trump, surprising his own staff, telephoned Mr. Duterte and invited him to visit the White House.

Mr. Trump’s gesture was widely condemned over concerns about human rights abuses in the Philippines carried out under Mr. Duterte’s auspices. In a sign of lingering tensions between the two countries, Mr. Duterte later said he might be too busy to make the trip.