The euro dropped to 1.4989 dollars in Tokyo morning trade, down from 1.5013 in New York late Friday. The euro slipped to 164.78 yen after 165.35.
The dollar fell to 109.96 yen from 110.11.
"Many players regard the unrest in Georgia as a new reason to sell the euro as Europe relies heavily on Russia for oil supplies," said Satoshi Tansho, a dealer at Chuo Mitsui Trust Bank.
Russia kept up its attacks on Georgia early Monday despite appeals for a ceasefire after Russian forces swept through the Georgian rebel region of South Ossetia.
Dealers said the euro was also weighed down by fading prospects of an interest rate rise by the European Central Bank (ECB) amid growing concerns about the health of the eurozone economies.
"The trend of selling the euro has not changed since last week," after the ECB acknowledged signs of weakening eurozone economic growth, reducing expectations of a rate rise to cool inflation.
The greenback eased below the 110 yen level on profit-taking, but many still see the dollar as "attractive at the current levels," Tansho said.
The US currency has fallen heavily over the past year as the Federal Reserve slashed interest rates to shore up the US financial markets and economy in the face of a housing slump and credit crunch.
But with concerns now growing that the eurozone and Japan could be heading for recessions, there is speculation that the greenback may have reached a turning point.
Italy on Friday reported a contraction in its economy in the second quarter. Japan is also expected to report on Wednesday that its economy shrank in the three months through June.
The Australian dollar hit a new seven-month low against the dollar on Monday, pressured by falling commodity prices.
The Australian dollar was "caught up in a wave of US dollar-buying related to mounting evidence that economic growth is slowing rapidly across the world," noted National Australia Bank market strategist John Kyriakopoulos.
The currency opened at 88.49 US cents, down from 89.29 US cents on Friday and its weakest start since January 25.