Rosenstein had appeared close to being fired following US media reports -- which he denied -- that he discussed secretly recording Trump and using the 25th constitutional amendment for removing presidents found to be unfit for office.
The pair spoke at length during a flight Monday to Florida, according to the White House.
Trump also indicated that he was ready to keep working with Rosenstein, saying "I actually have a good relationship." The president used the occasion to again insist that "there's been no collusion, folks, no collusion" with Russia.
Rosenstein, who oversees Mueller, has so far been steadfast in trying to protect the investigation as it digs ever deeper into Trump's inner circle.
So Rosenstein's departure -- possibly putting someone more pliable in his place -- would set off alarm bells over the future independence of a probe that could rock the entire presidency.
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