George W. Bush was the last Republican to occupy the White House before Donald Trump and faced harsh criticism during his time in office.
But asked in an interview with NBC if he ever considered the media the enemy of the people, the former president said it was important for a free press to hold people in power to account.
"I consider the media to be indispensable to democracy, that we need an independent media to hold people like me to account. I mean, power can be very addictive, and it can be corrosive, and it's important for the media to call to account people who abuse their power, whether it be here or elsewhere. One of the things I spent a lot of time doing was trying to convince a person like Vladimir Putin, for example, to accept the notion of an independent press. And it's kind of hard to tell others to have an independent, free press when we're not willing to have one ourself."
Mr Bush has backed calls for an investigation into alleged links between President Trump's election campaign and Russia.
Some rival Democrats have questioned whether officials in Mr Trump's campaign team had contact with Russian government officials before he became president.
Mr Trump was asked at a meeting with health insurance companies whether an independent investigator ought to be appointed to examine the matter.
He mouthed the word "No" as photographers were ushered out of the White House meeting, then could be heard speaking off-camera and saying, "I haven't called Russia in 10 years."
(Trump:) "Thank you very much."
(Aide:) "Thank you, everybody."
(Reporter:) "Mr President, do you support a special prosecutor on Russia?"
(Aide:) "Thank you. Thank you, press."
(Reporter:) "Do you support a special prosecutor on Russia?"
(Aide:) "Thank you, press."
(Another aide:) "Thanks very much."
(Trump, overheard:) "I haven't called Russia in 10 years."
The chairman of the US House of Representatives committee investigating possible ties with Russia, Devin Nunes, has insisted there is no need for a special prosecutor yet.
"What are we going to appoint a special prosecutor to do, exactly? To chase, to chase stories that ... of American citizens that end up in newspaper articles? I mean, that's ... right now ... I mean, look, if there is, at some point, we have serious crimes that have been committed, it would be something that we would consider. But at this point, we don't have that. The only serious crimes we have are leaks that have come out of ... of our government to the press and others."
Meanwhile, Mr Trump is seeking to boost defence spending by $US54 billion in his proposed budget plan for 2018.
The almost 10 per cent increase in military spending will be funded by cuts elsewhere in government, such as the foreign aid and environmental budgets.
But the President says his plan leaves large welfare programs such as Social Security and Medicare untouched, despite Republican calls for reform.
"This budget will be a public safety and national security budget, very much based on those two, with plenty of other things but very strong. And it will include a historic increase in defence spending to rebuild the depleted military of the United States of America at a time we most need it."
Mr Trump is expected to release his final budget proposal in mid-March.
