Weaker-than-expected economic data from China and Europe and fears of a possible US government shutdown spooked investors away from stocks toward the greenback and yen.
"The dollar is clearly showing it is attractive during times of market stress," said Ray Attrill, head of currency strategy at NAB in Sydney.
The dollar index, which gauges its value versus six major peers, was little changed at 97.44, below the 19-month high of 97.71 it hit on Friday.
The Australian dollar, whose fortunes are closely tied to China's economy, was marginally lower at $0.7174. It lost 0.3 percent of its value last week as data showed Chinese November retail sales grew at the weakest pace since 2003 and industrial output rose the least in nearly three years, underlining risks to the economy.
The offshore Chinese yuan was flat at 6.8974.
Apart from fears of a global economic slowdown, markets are also focussing on the likely trajectory of US monetary policy.
The Federal Reserve is set to raise interest rates by 25 basis points at its two-day meeting that opens Tuesday.
The central bank has lifted rates eight times since December 2015 in a bid to restore policy to more normal settings after having slashed borrowing costs to near zero to combat the financial crisis a decade ago.
With the hike largely factored in by the market, larger moves in the dollar will be guided by the Fed's forward guidance.
According to their projections in September, the median view among the Fed's policymakers was for three rate hikes in 2019. However, interest rate futures used to gauge the probability of further hikes are pricing in only one hike in 2019.
"Any content that speaks to the difference between market pricing of one interest rate rise in 2019 versus previous Fed indications of three rises is very likely to move markets," Michael McCarthy, Sydney-based chief markets strategist at CMC Markets, said in a note.
Traders believe that higher US borrowing costs will likely hurt US growth momentum and ultimately force the Fed to pause its monetary tightening path.
Recent comments by Fed officials have also been read as dovish by some analysts. Last month, Fed Chairman Jerome Powell said rates were near the range of policymakers' estimates of "neutral" - the level at which they neither stimulate nor impede the economy.
"The Fed will most likely move from an auto-pilot mode to being data dependent," said Attrill.
The dollar gained 0.1 percent over the yen in Asian trade to trade at 113.48. Interest rate differentials between the US and Japan make the dollar a more attractive bet than the yen, according to some analysts.
The Bank of Japan has a meeting on Dec. 19-20, at which policy is expected to remain highly accommodative as inflation remains well below the its target.
The euro was also little changed at $1.1310, having lost 0.6 percent last week after weaker-than-expected data out of France and Germany suggested that economic activity in Europe remains weak.
Sterling remained under pressure in Asian trade, down 0.02 percent at $1.2582. British trade minister Liam Fox said on Sunday talks with the European Union to secure "assurances" for parliament on Prime Minister Theresa May's Brexit deal will take time, with a decision expected in the new year.