“It is clearly unacceptable for any of our staff to be attacked for doing their job.”
Mr O’Donoghue said the goading of the crowds against the media is a “constant feature of these rallies”.
“I have been spat at before, they hurl abuse at American colleagues in particular,” he added.
The American president has a strained relationship with the media, and has often branded reporting as “fake news” and stated that journalists are “the true enemy of the people”.
The BBC’s Washington editor Eleanor Montague, who was also in the press gallery, said: “the crowd had been whipped up into a frenzy against the media by Trump and other speakers all night.’
During his speech on Monday, Mr Trump told the crowds inside El Paso County Coliseum that 69,000 people had signed up to attend.
“The arena holds 8,000 and thank you fire department, they got in about 10 (thousand),” he said.
“But if you really want to see something, go outside.
“Tens of thousands of people are watching screens outside.”
But according to reports, a spokesman for El Paso fire department said the president’s claim was incorrect, and that 6,500 people were allowed inside – the building’s capacity.