Donald Trump's relationship with Jeffrey Epstein has been pushed back into the spotlight after several years-old emails were released by the US president's opponents.

The emails were obtained by a congressional committee that has been investigating the Epstein case and how it was handled by authorities.

They were published by Democratic members of that committee, who say the emails suggest the White House has been hiding the truth about Mr Trump's relationship with the late convicted sex offender.

But Mr Trump says the move is part of a "hoax" designed to distract from the "massive damage" caused by the US government's record-breaking shutdown.

Now, as US politicians move to end the shutdown, Democrats — with the crucial support of four Republicans — are trying to force a new vote on the release of the so-called Epstein files.

Here's what the newly released emails tell us, and what happens next.

Email #1: Epstein says Trump spent hours with Epstein's accuser

The first of the emails show an exchange between Epstein and Ghislaine Maxwell, his partner and co-offender, who is now in prison for helping him abuse underage girls.

The exchange is dated April 2, 2011 — after Mr Trump and Epstein had purportedly ended their friendship.

In the first email, which contains multiple typos, Epstein wrote to Maxwell:

"i want you to realize that that dog that hasn't barked is trump.. [Redacted victim's name] spent hours at my house with him ,, he has never once been mentioned. police chief.