WASHINGTON — The White House’s guest list last week for President Trump’s first dinner celebrating the Muslim holy month of Ramadan included a who’s who of diplomats from the Middle East. But the event turned out to be more notable for who apparently was not there: representatives from Muslim American groups.

The night highlighted a paradox of Mr. Trump’s presidency. While he has sought to ally himself with Middle Eastern leaders, in part by at times softening his hostile tone on Islam, at home Mr. Trump has seemingly made little attempt to repair his fractured relationship with Muslim Americans — even those in his own party.

Saba Ahmed, the president of the Republican Muslim Coalition and a Trump supporter, said that at the outset of the presidency, there was a “complete shutdown of engagement” with Muslim Americans.

“It was quite a challenge” to work with Mr. Trump’s campaign staff, Ms. Ahmed said. “Even for the Republican Muslims who campaigned for him and helped him.”