Though oil prices pulled back slightly after surging to four-month highs on Monday, they remained about 15% higher than Friday's close as markets remain wary over the threat of a military response to attacks on Saudi Arabian crude oil facilities.
"The dollar is in demand as risk sentiment remains weak and it will be difficult for the Fed to overcome already dovish market expectations," said Manuel Oliveri, an FX strategist at Credit Agricole in London.
Traders widely expect the Fed will cut interest rates by a quarter of a percentage point on Wednesday, and one more cut is largely priced in before the end of 2019.
Against a basket of its rivals, the greenback edged up 0.1% to 98.66, heading towards a more than a two-year high of 99.37 earlier this month.
The Australian dollar led losers, falling 0.5% after the after the Reserve Bank of Australia flagged an easing bias in meeting minutes.
"They no longer talk about an accumulation of evidence in order to ease again, and highlight risks to the global economy," said National Australia Bank Senior FX Strategist Rodrigo Catril. "It certainly sounds a lot more dovish than before."
The drop in the Aussie also pulled the kiwi lower, with the New Zealand dollar weakening 0.4%. against the greenback.
The dollar's gains were also bolstered by an overnight spike in dollar funding costs.
The overnight rate in the repurchase agreement (repo) market jumped to 4.10% from 2.29% late on Friday, its highest levels seen since the start of the year. Analysts attributed the rise to quarterly federal tax payments and supplies.