In an interview with CBS News, Mr Blinken said the US did not want to hold China down but would not allow it to threaten the rules-based international order.
“I think that over time, China believes that it can be, and should be, and will be, the dominant country in the world,” the US official said on Sunday.
“What we’ve witnessed over the last several years is China acting more repressively at home and more aggressively abroad. That is a fact.”
Mr Blinken said China was behaving “increasingly in adversarial ways” but when questioned whether Washington was heading towards a military showdown with Beijing, he replied: “It’s profoundly against the interests of both China and the United States to get to that point, or even to head in that direction.”
Tensions have soared between Washington and Beijing over the past few years, with issues regarding human rights, espionage and the pandemic.
The China-US relationship is critical to both sides and the wider world, with Beijing frequently calling on the new administration in Washington to repair relations that fell apart under former president Donald Trump.
During the 60 Minutes interview, Mr Blinken emphasised that China is “the one country in the world that has the military, economic, diplomatic capacity to undermine or challenge the rules-based order that we care so much about and are determined to defend”.
“Our purpose is not to contain China, to hold it back, to keep it down; it is to uphold this rules-based order that China is posing a challenge to,” he said.
He added that the US doesn’t have the “luxury of not dealing with China," adding: “there are real complexities to the relationship, whether it’s the adversarial piece, whether it’s the competitive piece, whether it’s the co-operative piece."
Mr Blinken’s comments came after President Joe Biden, in his first address to Congress on Wednesday, said that he was not seeking conflict with China.
President Biden said he had told Chinese President Xi that "we welcome the competition" to be the dominant global power.
Mr Blinken arrived in London on Sunday for a G7 foreign ministers meeting where China is one of the issues on the agenda.