"We welcome anyone," Lin-Manuel Miranda told the BBC, adding that the American president-elect's daughter had seen the show and written "wonderful things".
Mr Trump demanded the cast of Hamilton apologise for addressing Mike Pence from the stage after Friday's show.
Miranda, however, insisted Mr Pence had been spoken to in a "respectful" way.
Vice President-elect Pence was booed by some audience members as he arrived at New York's Richard Rodgers Theatre on Friday.
Later, as he prepared to leave, he was asked by cast member Brandon Dixon to stay in the auditorium and listen to a brief address.
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"When we found out he was coming we welcomed him, we asked him to lead on behalf of all Americans and we related to him the anxieties that some of us feel," Miranda told the BBC.
"But I feel like we did it in a really respectful way."
Miranda went on to answer in the affirmative when asked if Mr Trump would be welcome to attend a Hamilton performance.
His comments, on Saturday, preceded Mr Trump's tweets criticising Mr Pence's treatment.
Miranda was a vocal supporter of Democratic candidate Hillary Clinton during the US presidential election.
The award-winning actor and writer, who gave up the title role in Hamilton earlier this year, is currently in London rehearsing for his role in Disney's upcoming Mary Poppins sequel.
Mr Pence's experiences at Hamilton prompted Mr Trump to lambast the Hamilton cast for their "terrible behaviour". He also suggested the show itself was "highly overrated".
His opinion, though, differs from that of his daughter Ivanka, who wrote that her "very high expectations" had been "surpassed" when she saw the musical in March.
Hamilton, a musical about America's first treasury secretary Alexander Hamilton, won 11 Tony awards in June and is one of the hottest tickets on Broadway.
The show, which has a multi-ethnic cast and a score made up of rap, hip-hop and R&B tracks, will open in London next year.
Miranda's music can currently be heard in Moana, a Disney animation about an adventurous Polynesian teenager, whose songs he co-wrote.
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The creator of Hamilton has said Donald Trump is welcome to attend his musical, the cast of which Trump attacked this week for "harassing" his running mate.