Ukraine has so far experienced its deadliest week since the separatist uprising began, leaving less room for peace efforts.
MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.6% after touching its lowest point since April 2. Japan's Nikkei lost 2.3%, tracking Tuesday's fall on Wall Street.
The dollar, which has lost about 0.5% against the yen so far this week, traded at 101.58 yen. A break below 101.32 would take the dollar to its lowest since Mar. 19.
The US currency was also on the back foot against the euro, which was boosted on Tuesday by upbeat PMI readings in Spain and Italy. The euro was at $1.3928, hovering within distance of an eight-week high of $1.3952 hit on Tuesday.
The US dollar index, which measures the greenback against six major currencies, stood at 79.12 after falling on Tuesday to 79.06, its lowest in more than six months.
"The point going forward is whether US stocks can retain their relatively steady footing should their European counterparts suffer from higher tensions in the Ukraine," said Junichi Ishikawa, market analyst at IG Securities in Tokyo.
"If US stocks can stay firm, it can help limit any selling stemming from the crisis to sporadic profit-taking and underpin global equity markets," he said.
The S&P 500 fell 0.9% on Tuesday but remains within striking distance of a record high hit a month ago.
Immediate focus for the dollar was on US Federal Reserve Chair Janet Yellen's congressional testimony later in the session.
Yellen is widely expected to maintain a dovish policy stance, doing little to arrest the recent fall of the dollar, which has shown a limited response to positive economic data.
"Fed Chair Yellen is likely to dodge any questions pertaining to the specific timing of interest rate rises, given the furore after her suggestion at a press conference in March that rates might rise about six months after asset purchases end," analysts at Capital Economics wrote in a note to clients.
Expectations that the Federal Reserve will not raise interest rates soon in addition to safe-haven bids have kept US Treasury yields low, hurting the dollar.
The US Treasury 10-year note yielded 2.587% after touching a three-month trough of 2.57% on Friday.
In the commodities markets, oil edged up after crude stocks decreased, defying expectations for an increase, with geopolitical risks helping put a floor under prices.
"The market is balancing a weak fundamental picture against the worry that we could see a disruption in Russian supplies," said Gene McGillian, analyst at Tradition Energy in Stamford, Connecticut.
US crude was up 0.6% at $100.05 a barrel.
Nickel hovered near a 15-month high as worries persisted about supply from major producers Russia and Indonesia, while stainless steel buyers also fuelled the rally.
Three-month nickel on the London Metal Exchange (LME) touched a session high of $18,700 a tonne, coming within grasp of a 15-month peak of $18,715 hit late in April.
Copper slipped amid worries of slowing growth in China, although signs that a US recovery is taking hold limited losses. LME copper slipped 0.4% to $6,695.75 a tonne.