Current sentiment among Chinese citizens is the U.S. should step back so Beijing can rise in power on the world stage, according to the head of a Washington-based consultancy's China operations.

"You had your time, this is our time," APCO's Greater China Chairman James McGregor told CNBC on Tuesday from Beijing, recalling comments from a ride-hailing driver in China. "'We are going to surpass America,'" the driver also said.

McGregor said on "Squawk Box" that China's communist government has been able to effectively rally its citizens as the world's two largest economies remain locked in a trade war. "They've got the population, and because they control the propaganda, they have the people pretty much geared up here that this is China's time," he added.

The U.S. and China have been involved in an escalating trade war over the past 15 months or so, with recent intentions to cement a "phase one" deal.

However, President Donald Trump said Tuesday it may be better to wait until the end of 2020 to make an agreement. Each side imposed tariffs on billions of dollars' worth of each other's goods, with the next deadline for new U.S. levies on Chinese products set for Dec. 15.

While tariffs have created a pain around the world, with both countries' economies experiencing ill-effects, McGregor said it's viewed as an inconvenience that Chinese citizens are willing to go through in order to better position themselves. They have a "we've got to get over this" mindset, feeling "this is the world trying to keep us down," he explained

Trump has often said that Beijing has been taking advantage of Washington.

On Tuesday, the president also told reporters at a NATO summit in London that China has been "ripping off the United States for many, many years."

The president has made similar remarks in the past. "Since China's entrance into the World Trade Organization in 2001, no one has manipulated better or taken advantage of the United States more," Trump said at a New York event last month. "I will not say the word 'cheated,' but nobody's cheated better than China, I will say that."