Asia markets were largely negative on Monday, with Canada and the U.S. failing to come to a trade agreement on Friday, and worries on further escalation in the U.S.-China trade war.

Japan's ended the first trading day of September in negative territory, down by 0.69 percent at 22,707.38 as most of its major sectors were lower. South Korea's Kospi also closed lower by 0.68 percent at 2,307.03.

In Australia, the ASX 200 reversed from its earlier gains to close 0.14 percent lower at 6,310.9.

The Greater China markets were down as Hong Kong's Hang Seng index fell 0.81 percent as of 2:59 p.m. HK/SIN. The mainland markets recovered from their earlier lows but still ended their trading day in negative territory, with the Shanghai composite lower by 0.17 percent at 2,720.74, and the Shenzhen composite down 0.169 percent to close at 1,448.93.

The moves in these markets came after the Caixin/Markit Purchasing Manager's Index (PMI), a private manufacturing survey, was released on Monday.The PMI came in at 50.6, its weakest value since June 2017, as export sales fell for the fifth consecutive month.

Some investors, however, say the slide in Chinese stocks is potentially unjustified.

"Companies that operate outside China, I think have been sort of, a bit unfairly hurt," said Erwin Sanft, managing director and senior portfolio manager at E Fund Management, on CNBC's "Squawk Box."

"There's been (this) assumption that, because we have trade disputes breaking out and being extended, that somehow these companies which do business outside China are all going to be hurt," he added.

In reality, Sanft said: "A lot of them are much more robust."

After going past a U.S.-imposed deadline last Friday for Canada to join a trade deal that had been reached between the U.S. and Mexico, more talks between Ottawa and Washington are set to continue this week.

U.S. President Donald Trump notified Congress last Friday that he wants to sign a trade agreement with Mexico, and potentially Canada, in 90 days — the legal period required for a deal to be reviewed.

And if trade tensions with China worsen, that might weigh on emerging market currencies.

"With heightened US-China trade tensions running in the background (with the consult on another $200bn of tariffs on China) any relief that NAFTA might present this Wed (assuming Canada reaches an agreement) could prove to be fleeting," said Vishnu Varathan, head of economics and strategy at Mizuho Bank.

"And if Trump tightens the screws on China, (emerging markets) risks could flare up again, with EM Asia currencies perhaps bearing the brunt of the burn," he added.

Echoing this sentiment, Gavin Parry, managing director at the Parry Group, told CNBC's "The Rundown" that "the trade side of things is still very much bringing a massive uncertainty to the table when it comes to, you know, underlying forecasts for growth."

Despite the trade tensions, stocks saw their best August performance in years over on Wall Street.

The Dow Jones Industrial Average ended Friday down by 22 points, but was still up 2.1 percent for the month. The closed 0.01 percent higher that day and was up by 3 percent for the month. Both the Dow and S&P 500 recorded their best performances for the month of August since 2014. The Nasdaq Composite saw even greater gains, closing Friday 0.26 percent higher and ending the month over 5.7 percent up — its best performance for August since 2000.

The U.S. dollar index, which tracks the greenback against a basket of currencies, was at 95.101 as of 2:57 p.m. HK/SIN, after reaching a low of around 94.52 last week.

The Japanese yen held on to its earlier gains against the dollar at 110.90 yen while the Australian dollar was largely flat at $0.7190 as of 2:58 p.m. HK/SIN.

– CNBC's Fred Imbert contributed to this report.