Oil prices have surged on expectations that global supplies would tighten due to fighting in Libya, OPEC-led cuts and U.S. sanctions against Iran and Venezuela, although energy prices slipped slightly on Tuesday.
As well as the Aussie and the loonie, the Norwegian crown also gained.
The Australian dollar rose 0.2 percent to $0.7144 after earlier touching a three-week high.
Canada's currency firmed to C$1.3293, its strongest since March 21.
"Themes such as U.S.-China trade talks and Brexit are turning rather stale and no longer providing the currency market with as much incentive. The rally in crude gave the market something to focus on under such conditions," said Bart Wakabayashi, Tokyo branch manager at State Street Bank.
The U.S. dollar fell for a second consecutive day while Washington's proposed list of tariffs on European goods had no immediate impact on the euro, with the single currency marginally higher.
Analysts, however, said they did not expect that to last.
"Even if these tariffs are going to have limited overall real economic impact they would nonetheless come at a bad moment, as the euro zone economy is already weakening," Commerzbank analyst Thu Lan Nguyen said.
"Any additional headwinds would further dampen the prospect of a rapid recovery and fuel speculation about further ECB measures. The euro is likely to continue struggling in this environment."
The euro rose 0.1 percent to $1.1266 with traders also preparing for Wednesday's European Central Bank meeting.
The dollar slipped 0.1 percent to 96.878, after losing 0.35 percent the previous day, marking its biggest daily decline since March 20.
Sterling edged towards $1.31 as Prime Minister Theresa May was set to ask German and French leaders for a Brexit delay amid a deadlock in London.
The Norwegian crown strengthened 0.1 percent to 8.541 per dollar after rallying 0.7 percent on Monday thanks to the higher oil price. It was also marginally up versus the euro .
The crown was also boosted after Norges Bank Governor Oeystein Olsen said on Monday that policymakers would continue to hike interest rates over the coming months, putting the bank in contrast to most that have pledged to keep rates low for longer in the face of weakening economic momentum.
The Japanese yen gained 0.1 percent to 111.355 yen per dollar.