In a speech in New York earlier this week, Mr Bush attacked “nationalism distorted into nativism” and said the country had “forgotten the dynamism that immigration has always brought to America”.
On the same day, speaking in Virginia, where was supporting Ralph Northam’s run for governor, Mr Obama said: “Instead of our politics reflecting our values, we have politics infecting our communities.”
While neither of the former presidents named Mr Trump, their comments were interpreted as being targeted at the current President. There is a convention that former occupants of the Oval Office do not criticise other presidents, so their remarks, from members of different political parties, were all the more powerful.
But White House press secretary Sarah Huckabee Sanders sought to deny the speeches were targeting Mr Trump.
“Our understanding is that those comments were not directed towards the president and, in fact, when these two individuals, both past presidents have criticised the president, they've done so by name and very rarely do it without being pretty direct, as both of them tend to be,” Ms Sanders told reporters in Washington, according to The Hill.
“So we will take them at their word that these actions and comments were not directed at the president.”
The news site said Ms Sanders did not respond to shouted questions about whether Mr Trump agreed with his predecessors’ belief that bigotry was on the rise.
Asked about Mr Bush’s comment that “politics seems more vulnerable to conspiracy theories and outright fabrications”, she hit back.
“If anybody is pushing a lot of fabricated things right now, I think most of that would be coming from the news media,” she said. “We would certainly agree with that sentiment.”