Trump, in two tweets late Sunday, accused China of keeping its currency artificially low and of military posturing in the South China Sea -- home to a tense territorial dispute.
"Did China ask us if it was OK to devalue their currency (making it hard for our companies to compete), heavily tax our products going into their country (the US doesn't tax them) or to build a massive military complex in the middle of the South China Sea? I don't think so!," Trump said on Twitter.
Trump appears to be pushing back against critics
, who say his shoot-from-the-hip diplomatic style risks a confrontation with China.
Beijing regards Taiwan -- officially the Republic of China -- as a breakaway province and has said it will use military force against the island if necessary. The two sides split in 1949 after Communist victory in the civil war.
The 10-minute conversation with President Tsai Ing-wen, which Trump described as a congratulatory call, was the first time a US president has spoken to Taiwan's leader since Washington established diplomatic relations with Beijing in 1979.
It's unclear to what extent Trump's latest comments will rattle Beijing, which had a fairly muted stance to Friday's phone call.
Foreign Minister Wang Yi said Saturday it was a petty gambit and China lodged an official complaint.
A front-page opinion piece published Monday on the overseas edition of the People's Daily -- the Communist Party's official mouthpiece -- said the call set a bad precedent.
"Trump's unconventional move on Taiwan did ring a warning bell for the direction of Sino-US relations. China will not take it lightly," the paper said.
Lu Kang, a spokesman for China's Ministry of Foreign Affairs, declined to comment specifically on the latest tweets. He said Monday that China didn't comment on a politician's style or personality and only cared about their policies.
"The whole world is clear on the Chinese government's position on Taiwan, and that includes President-elect Trump and his team," Lu said, adding that China maintains contact with President-elect Trump and his team.
Victor Gao, a Chinese international relations expert and former translator to late Chinese paramount leader Deng Xiaoping, said that Trump could say what he liked as President-elect but his comments would have huge global consequences once in office.
"We hope President-elect Donald Trump, who will very soon go into (the) White House, will handle himself with respect, accountability and responsibility and become a force of peace and stability rather than making whimsical and capricious remarks aimed at surprising the world," he said.
Trump's remarks on China's currency aren't dramatically different from his campaign trail rhetoric
, however, it's only the second time that Trump has weighed in on the South China Sea dispute.
Tensions have ratcheted up in the waters, which are a major shipping route, as China has conducted massive dredging operations to reclaim land around territory it controls, turning sandbars into islands equipped with airfields, ports and lighthouses.
Beijing has also warned US warships and military aircraft to stay away from these islands.
It was unclear to what extent the phone call with Tsai signaled a considered shift in US-China policy by Trump and his transition team.
Trump tweeted that Tsai had called him but Taiwan's Presidential spokesman Alex Huang told CNN that both sides agreed ahead of time before making contact, but would not give any further details including exactly when they agreed to the call.
Christopher Hill, a former US ambassador, said that Trump was "winging it" and may not have been aware of the significance of the move.
"It was an example of what is all too often happening now with this incoming administration, this tendency to wing it," he told CNN's Erin Burnett. "What I'm concerned about is that rather than acknowledge a mistake, they will double down on it."
But criticism hasn't been universal. Others have welcomed the prospect of better ties with Taiwan -- a boisterous, multi-party democracy that stands in sharp contrast to China, a one-party state whose rulers are tightening their grip on dissent.
Michael Pillsbury, a China adviser to Trump during the campaign who served under Presidents Ronald Reagan, George W. Bush and Obama, said Trump's call was like many of the dozens he had made and taken since Election Day with world leaders.
"It shouldn't be seen as a departure from norms," Pillsbury said.
"We should have warmer ties with Taiwan. And it can be done without alienating Beijing. Indeed over the last decade, Taipei has pursued closer relations with the mainland. We too can do both. The zero sum mentality is an old way of thinking."