Exchanges were generally thin with markets in London and Tokyo closed for public holidays.
However, the dollar remained strong on expectations that the Federal Reserve will stick to the path of aggressive interest rate hikes to contain high inflation.
The dollar index, which measures the performance of the US currency against six competing currencies, rose 0.4 percent to 110.06, heading to record its highest level in 20 years of 110.79, which it recorded on the seventh of September.
Markets expect a US interest rate hike of 75 basis points this week, with about a 20 percent chance of a 100 basis point increase.
The euro fell 0.4 percent to $ 0.9972 and the pound sterling fell 0.3 percent to $ 1.1390 and remained close to its lowest level in 37 years recorded on Friday, while both the New Zealand dollar and its Australian counterpart fell by more than 0.5 percent.
Markets are divided over whether the BoE will raise rates by 50 or 75 basis points on Thursday.
The Canadian dollar fell in early European trade to its lowest level in almost two years at 1.3311 against the US dollar.
The dollar rose 0.4 percent to 143.46 yen, hovering below the strong resistance level at 145 which was boosted by hawkish Japanese policy makers’ talk of currency intervention.
And the Chinese yuan remained weak at around seven against the dollar as economic concerns loom and the possibility of further cuts in benchmark interest rates next Tuesday.
Bitcoin, the largest cryptocurrency by market capitalization, fell to a three-month low below $19,000, as concern over global interest rate hikes hurt risky assets.