The U.S. dollar was higher against its major opponents in the Asian session on Monday, as U.S. President Donald Trump claimed "big progress" in trade talks with China, easing fears over a trade war that would hurt global growth.

Trump held telephonic conversation with Chinese president Xi Jinping on Saturday and claimed "big progress" towards a deal.

"Deal is moving along very well. If made, it will be very comprehensive, covering all subjects, areas and points of dispute. Big progress being made!," Trump tweeted.

Chinese news agency Xinhua cited President Xi Jinping as saying that both the nations aimed to achieve "stable progress" in ties.

The Bloomberg said, citing two people familiar with the matter that a U.S. government delegation would travel to Beijing in the week of Jan. 7 to hold the first face-to-face trade talks with Chinese officials since Trump and China's Xi Jinping agreed on a 90-day truce in Argentina earlier this month.

Traders awaited developments in Washington after political commentators suggested an agreement to end the partial government shutdown is unlikely to be reached before Democrats take control of the House next Thursday.

The U.S. economic calendar for this week starts off relatively quiet, although the Labor Department's monthly jobs report is likely to be in focus later in the week.

The greenback appreciated to 0.9859 against the franc, following a decline to 0.9828 at 5:15 pm ET. If the greenback extends rise, 1.00 is likely seen as its next resistance level.

The greenback advanced to a 4-day high of 1.1422 against the euro, after having dropped to 1.1450 at 7:40 pm ET. The greenback is seen finding resistance around the 1.13 mark.

After falling to 1.2703 against the pound at 6:00 pm ET, the greenback reversed direction and moved up to 1.2680. The greenback is likely to test resistance around the 1.25 region.

The greenback reached as high as 110.48 against the yen and held steady thereafter. At last week's close, the pair was worth 110.25. On the upside, the greenback is likely to challenge resistance around the 112.00 level.

On the flip side, the greenback declined to 4-day lows of 0.6721 against the kiwi and 0.7070 against the aussie, from its early highs of 0.6703 and 0.7042, respectively. Next key support for the greenback is seen around 0.685 against the kiwi and 0.725 against the aussie.

The greenback reversed from an early high of 1.3638 against the loonie, falling to 1.3611. The next possible support for the greenback is seen around the 1.35 area.

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