Russia and China are "rival powers", Trump said, but the US must attempt to build a "great partnership with them".
As an example of this new spirit of co-operation, Mr Trump referred to a phone call of thanks he received from Russian President Vladimir Putin for intelligence the CIA provided to the Kremlin about an alleged terror plot.
Mr Trump described "four pillars" to his new plan but made no mention of human rights or climate change, his critics noted.
The four themes are protecting the homeland, promoting American prosperity, demonstrating peace through strength and advancing American influence.
The 68-page document, which White House officials began work on 11 months ago, suggests a return to Mr Trump's campaign promises.
It explicitly states that "the United States will no longer turn a blind eye to violations, cheating or economic aggression".
As it was reported earlier Vladimir Putin, the President of Russia held the phone talk with Donald Trump, the President of the US on December 17 to thank him for the work of the Central Intelligence Agency (CIA) that prevented the number of bombings in St. Petersburg.
The Russian president expressed his gratitude to the CIA and noted that it allowed the Russian authorities to prevent the attack at the Kazan Cathedral and other crowded places. Putin added that the CIA information was enough to find and detain the terrorists.