Democratic presidential contenders have criticised US President Donald Trump for promoting a conspiracy theory about the apparent suicide of disgraced financier Jeffrey Epstein in his New York jail cell.

Key points: Mr O'Rourke accused Mr Trump of trying to shift the public's focus away from recent mass shootings

Mr O'Rourke accused Mr Trump of trying to shift the public's focus away from recent mass shootings The FBI and the Department of Justice's inspector general have opened investigations into Mr Epstein's death

The FBI and the Department of Justice's inspector general have opened investigations into Mr Epstein's death Mr Trump has a history of promoting conspiracy theories about political rivals

After Saturday's death of Mr Epstein, a millionaire charged with sex trafficking who once counted Mr Trump and former president Bill Clinton as friends, Mr Trump retweeted a claim from a conservative comedian that Mr Clinton was involved in the death.

Mr Trump retweeted Terrence K Williams, who said Mr Epstein "had information on Bill Clinton & now he's dead".

The move drew criticism from Beto O'Rourke, a former congressman from Texas, speaking on CNN's State of the Union.

"This is another example of our President using this position of public trust to attack his political enemies with unfounded conspiracy theories," Mr O'Rourke said.

Mr O'Rourke said Mr Trump was trying to shift the public's focus away from last weekend's mass shootings in El Paso, Texas, and Dayton, Ohio, which have led to new calls for gun restrictions and criticism of Mr Trump's divisive anti-immigrant and racially charged rhetoric.

"He's changing the conversation, and if we allow him to do that then we will never be able to focus on the true problems, of which he is a part," Mr O'Rourke said from his hometown of El Paso.

Cory Booker, a US senator from New Jersey, said Mr Trump's retweet was "just more recklessness".

"He is giving life to not just conspiracy theories but really whipping people up into anger and worse against different people in this country," he said on CNN.

White House senior adviser Kellyanne Conway said Mr Trump's retweeting showed "the President just wants everything to be investigated".

"It's not for me to go further than where the DOJ [Department of Justice] and FBI are right now," she said.

Two investigations underway into Epstein's death

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 33 seconds 33 s A van reportedly carrying Jeffrey Epstein's body leaves a hospital.

The FBI and the Department of Justice's inspector general have opened investigations into the death of Mr Epstein, who a source said had been taken off suicide watch.

Last month, Mr Epstein was found unconscious on the floor of his jail cell, and officials were investigating that incident as a possible assault or attempted suicide.

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US Attorney-General William Barr said he was "appalled" to learn of the apparent suicide in federal custody.

"Mr Epstein's death raises serious questions that must be answered," Mr Barr said in a statement on Saturday.

Alexandria Ocasio-Cortez, a Democratic congresswoman from New York City and a leading progressive voice, tweeted: "We need answers. Lots of them."

Ms Conway said the investigation of Mr Epstein should continue despite his death.

"Jeffrey Epstein has done some very bad things over a number of years, so let's continue to investigate that," she said on Fox News.

"I don't think that somebody's crimes and the accountability for that necessarily perish with them."

'This is a very dangerous President'

The Metropolitan Correctional Center where Jeffrey Epstein was being held. ( Reuters: Jeenah Moon )

More than a decade ago, Mr Epstein pleaded guilty in Florida to state charges of solicitation of prostitution from a minor in a deal with prosecutors that has been widely criticised as too lenient.

Then in July, Mr Epstein was indicted, with federal prosecutors in New York accusing him of knowingly recruiting underage women to engage in sex acts with him, sometimes over a period of years while paying the women for each encounter. He pleaded not guilty.

Mr O'Rourke and Mr Booker are among two dozen candidates seeking the Democratic nomination to challenge Republican Mr Trump for the White House in 2020.

Nearly all of those Democrats have condemned Mr Trump's rhetoric for inflaming racial tensions and anger.

"We've seen people's lives being threatened because this President whips up hatred. This is a very dangerous President that we have now," Mr Booker said.

Mr Clinton's spokesman, Angel Urena, blasted Mr Trump for giving oxygen to the conspiracy by retweeting Williams.

"Ridiculous, and of course not true — and Donald Trump knows it. Has he triggered the 25th Amendment yet?" he said, referring to the procedures for replacing a president.

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Mr Trump has a history of promoting conspiracy theories about political rivals. Even before he was a presidential candidate, Mr Trump repeatedly questioned whether former president Barack Obama was born in the United States, even after Mr Obama produced a birth certificate proving he was.

During the Republican presidential nomination race in 2016, Mr Trump spread an unfounded conspiracy theory linking the father of rival US senator Ted Cruz to the assassination of former president John Kennedy, a claim Mr Cruz denounced as a lie.

A courtroom artist's sketch of Jeffrey Epstein appearing in New York federal court.. ( AP: Elizabeth Williams )

Reuters