He said: “I think President Obama’s behind it because his people are certainly behind it”, but added: “I also think it’s just politics.”
President Trump offered no evidence for his claims and his predecessor in the White House has not commented.
He also spoke about his budget plans and other issues.
The president’s interview was broadcast hours before he is due to give his first address to a joint session of Congress.
In the speech he is expected to set out in greater detail his plans to cut spending and boost the economy.
Donald Trump has said his proposal to increase the defense budget by $54 billion would be paid for by a “revved up economy”.
The foreign aid purse and the environmental department face a squeeze to pay for it, but analysts are doubtful the spending promises can be kept without increasing the deficit.
President Trump said he would get “more product for our buck” in terms of buying military hardware and would ask for a “form of reimbursement” from countries making use of the US military.
In the Fox News interview, President Trump was asked about the protests faced by some Republican politicians at town hall meetings across the country.
The president said he was certain Obama loyalists were behind both those protests and White House leaks.
“In terms of him being behind things, that’s politics. And it will probably continue,” Donald Trump added.
The president was asked for more detail on how he would find the money for the 10% increase in military spending he has proposed for 2018. Proposed cuts elsewhere are unlikely to cover the proposed increase.
The White House sent Donald Trump’s 2018 budget blueprint, which begins on October 1, to federal agencies on February 27.
The agencies will then review the plan and propose changes to the cuts as the White House prepares for negotiations with Congress.
The Republican-controlled Congress must approve any federal spending.
Donald Trump’s plan is expected to face a backlash from Democrats and some Republicans over the planned cuts to domestic programs.
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