China announced plans on Friday to lift some tariffs on USA soybeans and pork.
USA stocks pulled back on Monday from near-record levels, as Apple and healthcare shares fell and investors braced for a busy week of political and economic news, including a potential turning point in the U.S.
Meanwhile, China's exports shrank for the fourth consecutive month in November, sending shivers through a market already concerned about damage being done to global demand by the trade war.
According to a survey of its members released Monday, 64 percent of respondents said they have not noticed "any change" in their business as a result of the trade war.
The benchmark Shanghai Composite Index added 0.08 per cent, or 2.45 points, to 2,914.46 and the Shenzhen Composite Index, which tracks stocks on China's second exchange, rose 0.23 per cent, or 3.83 points, to 1,644.16.
Chinese exports fell in November as country's bitter trade war with the United States continued to weigh on the economy, although import growth did come in ahead of economists' forecasts.
The Canadian dollar traded at C$1.3255 to the U.S. unit.
In Asia, Japan's benchmark Nikkei 225 edged 0.3% higher to finish at 23,430.70, after the Cabinet Office reported the economy expanded at a 1.8% annual pace in July-September, spurred by strong consumer purchases ahead of an October 1 sales tax hike.
The weak start to the week came despite data showing China's crude imports jumped to a record, revealing just how deep jitters are embedded in the market over the US-China trade row that has stymied global growth and oil demand.
Celtics' Marcus Smart suffers abdominal injury vs the Knicks
If he's able to raise his shooting percentage and overall game, it would make future Knicks roster decision-making a lot easier. The C's won the first game at MSG by 23 points before prevailing in a much close two-point contest at TD Garden six days later.
The report comes ahead of the Federal Reserve's two-day meeting that begins Tuesday.
On the phase-one trade deal, top White House economic advisor Larry Kudlow told Bloomberg Television on Friday that officials were talking round the clock and that two countries were attempting to agree on the quantum of American agricultural purchases by China.
Analysts said the much better-than-expected jobs report offset mixed signals from recent economic data and validated the Fed's wait-and-see stance on interest rates after three "insurance cuts" this year.
Maruti Suzuki India Ltd will be in focus as the company, after nine straight months of falling production, built more vehicles in November than a year earlier, following the mild sales recovery seen in the festive month of October.
OPEC and allies officially agreed on Friday to cut production by an additional 500,000 barrels per day beginning next month.
The U.S. dollar, which bounced on Friday after data showed U.S. job growth increased in November by the most in 10 months, was down marginally against a basket of currencies .DXY and the euro, at $1.107 EUR=EBS .
In currencies, the dollar fell to 108.47 Japanese yen from 108.59 yen on Friday.
Elsewhere, sterling traded at $1.3143, not far from a seven-month high of $1.3166 set on Thursday.