WASHINGTON — When President Trump called President Rodrigo Duterte of the Philippines on Saturday, the American leader’s national security aides saw it as part of a routine diplomatic outreach to Southeast Asian leaders. Mr. Trump, characteristically, had his own ideas.

During their “very friendly conversation,” the administration said in a late-night statement, Mr. Trump invited Mr. Duterte, an authoritarian leader accused of ordering extrajudicial killings of drug suspects in the Philippines, to visit him at the White House.

Now, administration officials are bracing for an avalanche of criticism from human rights groups. Two officials said they expected the State Department and the National Security Council, both of which were caught off guard by the invitation, to raise objections internally.

The Run-Up

The podcast that makes sense of the most delirious stretch of the 2016 campaign.

The White House disclosed the news on a day when Mr. Trump whipped up ardent backers at a campaign-style rally in Harrisburg, Pa. The timing of the announcement — after a speech that was an angry, grievance-filled jeremiad — encapsulated this president after 100 days in office: still ready to say and do things that leave people, even on his staff, slack-jawed.

“By essentially endorsing Duterte’s murderous war on drugs, Trump is now morally complicit in future killings,” said John Sifton, the Asia director of Human Rights Watch. “Although the traits of his personality likely make it impossible, Trump should be ashamed of himself.”

Administration officials said the call to Mr. Duterte was one of several to Southeast Asian leaders that the White House arranged after picking up signs that they felt neglected because of Mr. Trump’s intense focus on China, Japan and tensions over North Korea. On Sunday, Mr. Trump spoke to the prime ministers of Singapore and Thailand.

Mr. Duterte’s toxic reputation had already given pause to some in the White House. The Philippines is to host a summit meeting of the Association of Southeast Asian Nations in November, and officials said there was a brief debate about whether Mr. Trump should attend.

It is not even clear, given the accusations of human rights abuses against him, that Mr. Duterte would be granted a visa to the United States were he not a head of state, according to human rights advocates.

Still, Mr. Trump’s affinity for Mr. Duterte — and other strongmen — is well established. Both presidents are populist insurgent leaders, with a penchant for making inflammatory statements. Both ran for office calling for a wholesale crackdown on Islamist militancy and the drug trade. And both display impatience with the courts.

After Mr. Trump was elected, Mr. Duterte called to congratulate him. Later, the Philippine leader issued a statement saying that the president-elect had wished him well in his antidrug campaign, which has resulted in the deaths of several thousand people suspected of using or selling narcotics, as well as others who may have had no involvement with drugs.

Interactive Feature | ‘They Are Slaughtering Us Like Animals’ Inside President Rodrigo Duterte’s brutal antidrug campaign in the Philippines, our photojournalist documented 57 homicide victims over 35 days.

Mr. Trump’s cultivation of Mr. Duterte has a strategic rationale, officials said. Mr. Duterte had pivoted away from the United States, a longtime treaty ally, and toward China. The alienation deepened after he referred to President Barack Obama as a “son of a whore” when he was asked how he would react if Mr. Obama raised human rights concerns with him.

In October, Mr. Duterte called for a “separation” between the Philippines and the United States. “America has lost now,” he told an audience of business executives in Beijing. “I’ve realigned myself in your ideological flow.” He later threatened to rip up an agreement that allows American troops to visit the Philippines.

Administration officials said Mr. Trump wanted to mend the alliance with the Philippines as a bulwark against China’s expansionism in the South China Sea. The Philippines has clashed with China over disputed reefs and shoals in the waterway, which they share.

Mr. Trump, these officials said, admires Mr. Duterte’s fierce words on fighting Islamist extremists who have terrorized the southern islands of the Philippine archipelago. Mr. Duterte once declared that if he were presented with a suspected terrorist, “give me salt and vinegar and I’ll eat his liver.”

The two leaders are also in tune on the need for a crackdown on drugs, even if Mr. Trump is not advocating Mr. Duterte’s brutal methods. Attorney General Jeff Sessions has revived the language of the “war on drugs” that the Obama administration shunned as part of its policy to reduce lengthy prison sentences for nonviolent drug offenders.

Beyond that, there is Mr. Trump’s instinctive affinity for strongmen. Two weeks ago, he called to congratulate President Recep Tayyip Erdogan of Turkey for his victory in a much-disputed referendum expanding his powers, which some critics painted as a death knell for Turkish democracy.

The White House description of the call made no mention of whether Mr. Trump had raised reports of voting irregularities during the referendum or the government’s heavy-handed tactics in the weeks leading up to it. The State Department noted both concerns in a more circumspect statement issued a few hours earlier.

Mr. Trump has also praised President Xi Jinping of China for his cooperation in pressuring the rogue regime in North Korea, even though Mr. Xi has cracked down on dissent and emerged as the most powerful leader China has had since Mao Zedong.

“The relationship I have with China,” Mr. Trump said in an interview that aired on Sunday on the CBS program “Face the Nation,” “it’s been already acclaimed as being something very special, something very different than we’ve ever had.” Mr. Xi, he added, is a “very respected man.”

Mr. Trump played host at the White House to the Egyptian president, Abdel Fattah el-Sisi, who had not been granted an invitation since he seized power in a military coup nearly four years ago. Mr. Trump credited his relationship with Mr. Sisi as a factor in obtaining the release of an Egyptian-American aid worker, Aya Hijazi, who had been detained in Egypt.

Finally, there is Mr. Trump’s vow during the presidential campaign to pursue a warmer relationship with President Vladimir V. Putin of Russia. That effort has faltered somewhat because of persistent questions about links between the Trump campaign and Russian officials.