Members of a migrant “caravan” heading north through Mexico paused on Tuesday to pay their respects to two of their fellow travellers who have died en route, as hundreds turned back from the perilous journey to the US border.
Mike Pence, the US vice president, said he had been told by Juan Orlando Hernandez, president of Honduras, that the migrant caravan was being "financed by Venezuela."
“And by the Democrats?” asked Mr Trump, seated at his desk in the Oval Office.
The crowd laughted uneasily.
“It has been organised by Leftist groups," said Mr Pence, after a pause.
Mr Pence re-stated Mr Trump’s unproven claim that there were “unknown Middle Easterners” among the 7,000 migrants.
“It’s inconceivable that there are not people of Middle Eastern descent in a crowd of more than 7,000 people advancing toward our border,” he said.
“In the last fiscal year, we have apprehended more than 10 terrorists or suspected terrorists per day at our southern border.”
In the year to September 30, over 300,000 people were detained at the US-Mexico border, of whom 0.02 per cent – 61 people – were from countries in the Middle East. None of the reporters following the caravan have met anyone of Middle Eastern descent.
Pressed on whether there were people from the Middle East in the caravan, Mr Trump said: "There is no proof of anything, but there may well be."
Yet the claims are being frequently repeated on Fox News, as Mr Trump and his supporters watch his ratings rise with his repeated rants against the caravan.
On Monday night, Mr Trump called the caravan an “assault on our country” and suggested, without citing evidence, that “Democrats had something to do with it.”
He added: “We need a wall built fast.”
The government of Honduras, from where the caravan set out on October 13, announced on Monday that 300 people had elected to turn back. A further 150 had abandoned the march the previous day, taking up the government’s offer of flights and buses back to their country.
The country’s official Twitter stream showed images of exhausted-looking migrants on drips, being tended to by Red Cross personnel, or boarding buses to head home. Ana Garcia de Hernandez, the first lady of Honduras, published a video begging her fellow citizens not to carry on their dangerous path.
Two Hondurans have died so far, both falling off trucks – one on Saturday, and one on Monday.
“This person had a dream,” said one of the caravan’s leaders, addressing the crowd in the Mexican town of Huixtla, 35 miles north of the Guatemalan border.
“They suffered, we know this is the route of death, where a lot of people have died. Everyone, please light a candle in your homes, in memory of them.”
The caravan paused on Tuesday in respect for the dead.
On Wednesday organisers plan to continue, heading north along the coast to the town of Mapastepec, 38 miles away.