Spokeswoman Sarah Huckabee Sanders called for supporters to behave “in a peaceful and respectful manner,” amid criticism of Mr Trump for whipping up his crowds over supposed media bias.
Cameraman Ron Skeans was repeatedly shoved from behind by a man in a Make America Great Again Hat who climbed on to the press platform at the president’s rally in El Paso on Monday. Mr Skeans, from Ohio, was not seriously hurt.
The BBC’s Washington news editor, Eleanor Montague, said the crowd "had been whipped up into a frenzy against the media" by the president and other speakers before an attack which the broadcasters’s Washington correspondent, Gary O’Donoghue, described as “incredibly violent”.
Paul Danahar, the BBC’s Americas bureau chief, said the media area had been unsupervised and security failed to intervene. He has written to Ms Huckabee Sanders “asking for a full review of security arrangements for the media”.
The White House press secretary did not address Monday’s attack directly but said the president “condemns all acts of violence against any individual or group of people - including members of the press".
She added: "We ask that anyone attending an event do so in a peaceful and respectful manner."
“The attacks on the media are hugely popular with his supporters,” wrote Jon Sopel, the BBC’s North America editor, on Tuesday.
“They are every bit as much a part of his ‘set’ as Honky Tonk Woman and Satisfaction are part of a Rolling Stones concert. You just can't imagine it not happening.”
The White House News Photographers Association, of which Mr Skeans is a member, accused the president of “inciting violent acts such as this one”.
It said in a statement: “Given that the president's rhetoric about journalists is too often false and derogatory, we ask that he refrain from unnecessarily targeting journalists.”
The UK's foreign secretary, Jeremy Hunt, said the government was "very worried" about violence against journalists.
"It is never acceptable when journalists and cameramen are attacked just for doing their job," he told Sky News on Tuesday. "There is a broader issue here which is that last year 80 journalists were killed across the world just for doing their job."
Mr Trump was also condemned by the Committee to Protect Journalists, which said it was “outrageous that a journalist was attacked while covering a presidential speech”.
Alexandra Ellerbeck, the organisation’s North America programme coordinator, added: "We call on President Trump to moderate his rhetoric against the press and to state clearly that physically attacking media personnel is not acceptable."
Mr Trump was challenged about his "potentially dangerous" anti-media rhetoric by AG Sulzberger, publisher of The New York Times, in an interview earlier this month.
The president claimed he had "great respect for the press" but complained he was not "treated fairly".