Americans need to stop buying products made in China because other punitive measures in the trade war haven't been effective, Sen. Rick Scott told CNBC on Monday.

"I think we ought to spend all our time thinking about how do we buy American products," the Florida Republican said on "Squawk Box."

"Stop buying Chinese products. That will have the biggest impact on their economy. That's the only thing that will force them to change what they're doing. They don't feel the pressure yet to change."

The U.S. and China have been engaged in an escalating trade war for the past year, with each side upping retaliatory tariffs over the summer. The largest hike in duties took place earlier this month before Washington and Beijing agreed to meet for another round of high-level talks in October.

Representatives of the world's two largest economies also met last week to lay the groundwork for those renewed negotiations. The Chinese state news agency Xinhua said the discussions were "constructive."

Chinese representatives did, however, cancel a planned trip to Montana and Nebraska that was intended to build goodwill with American farmers.

Scott said he understands the U.S. consumer has, in many ways, benefited from the growth in Chinese manufacturing because it has lowered the costs of goods. Even so, Scott said it's time to look elsewhere.

"There's other countries to do business with," Scott said. He said unlike China, those countries are not trying "annihilate."

Scott said the reason he is arguing for Americans to stop buying Chinese products is because steps taken by President Donald Trump's administration haven't yielded change, though he described tariffs as the "only leverage" the U.S. has.

He said China isn't complying with World Trade Organization rules and has failed to fulfill its January promise to buy American soybeans. He also criticized China's record on human rights.

"We have to stand up to China," Scott said. "We don't have a choice. They've killed our jobs, they're killing people with the fentanyl. They're stealing technology. They're not a good player."

China denies it's the source of the fentanyl that's killing Americans, contrary to Trump's tweets.