Democratic presidential hopeful Pete Buttigieg Pete ButtigiegThe Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November Buttigieg stands in as Pence for Harris's debate practice Hillicon Valley: FBI, DHS warn that foreign hackers will likely spread disinformation around election results | Social media platforms put muscle into National Voter Registration Day | Trump to meet with Republican state officials on tech liability shield MORE on Friday night accused President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE of "paying lip service" to LGBT rights after Trump said he was "absolutely fine" with Buttigieg appearing onstage with his husband.

"Even though they’re paying lip service to the idea of -- like the president was asked about my marriage, so he could have the opportunity to say he’s fine with it," Buttigieg said while speaking in Iowa, according to ABC News. "That’s nice."

The South Bend, Ind. mayor referenced a Daily Beast report from this week that says adopted children of LGBT families may now be considered born "out of wedlock" and not guaranteed U.S. citizenship even if their parents are married U.S. citizens.

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"We find out this week that they changed the State Department guidance -- I don’t know if you saw this," Buttigieg said, according to ABC. "So if you are, for example, in an international adoption scenario, and you’re a same-sex couple, as far as the United States government is concerned, you have a child born out of wedlock. Think about what that means. It means you are not a citizen of the same country as your own child at the time that they are born. And that’s discrimination."

Trump said in a clip for a Fox News interview that will air Sunday that he thinks it is "great" that Buttigieg appears with his husband Chasten.

"I think it's absolutely fine. I do," the president told Fox. "I think it's great. I think that's something that perhaps some people will have a problem with. I have no problem with it whatsoever."

Buttigieg has been critical of Vice President Pence's stances on LGBT issues. He told conservative radio host Hugh Hewitt on Friday that Pence "advances homophobic policies."

In response to prior criticism from Buttigieg, Pence has said that the mayor "knows I don't have a problem with him."

"I don't believe in discrimination against anybody. I treat everybody how I want to be treated," the vice president and former Indiana governor said in a CNN interview last month. "The truth of it is all of us have our own religious convictions. Pete has his convictions. I have mine."

Buttigieg has said that he is not critical of Pence's faith but rather of his "bad policies."

Buttigieg is among two dozen people vying for the Democratic Party's 2020 presidential nomination.