Trump told The Wall Street Journal in an interview published Friday that he would keep intact "at least for a period of time" sanctions President Barack Obama's administration imposed on Russia last month over Moscow's alleged cyberattacks to influence the US election.
But, if Russia helps the US on key goals such as fighting violent extremists, Trump suggested he may scrap the punitive measures altogether.
He also said he was prepared to meet with Russian President Vladimir Putin after taking office January 20.
Turning to the longstanding US practice of not recognizing Taiwan diplomatically, Trump said: "Everything is under negotiation, including One China."
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Trump has already irked China by accepting a congratulatory phone call from Taiwan's President Tsai Ing-Wen after he won the election, upending decades of diplomatic precedent in which the White House has foregone direct communication with the island's leader.
He defended that move in his interview with the Journal, saying: "We sold them 2 billion of military equipment last year. We can sell them $2 billion of the latest and greatest military equipment but we're not allowed to accept a phone call. First of all, it would have been very rude not to accept the phone call."
Trump has threatened to get tough with what he sees as unfair Chinese trade practices, and suggested that the "One China" policy could become a bargaining chip in other disputes.