In morning European trading the euro bought US$1.4226 after touching a new all-time high of US$1.4283 early in Asia before slipping back. It was still up from the US$1.4160 it bought late on Friday in New York.
The British pound rose slightly to US$2.0466 from US$2.0454 late Friday, while the dollar rose to purchase 115.47 Japanese yen from 114.74 in New York.
The Canadian dollar, which hit a 31-year high versus the U.S. dollar on Friday of US$1.0091, was down to US$0.9935.
Markets were looking ahead to the Arizona-based Institute for Supply Management's factory index release later in the day for indications as to what the U.S. Federal Reserve's next interest rate move might be.
The Fed is widely expected to cut rates again for the second month in a row in October in an effort to stimulate the flagging U.S. economy.
The dollar's strength was broadly hurt after the Fed last month cut rates by a larger-than-expected half percentage point.
The lower U.S. interest rates, used to jump-start the economy, can weaken its currency as investors transfer funds to countries where their deposits and fixed-income investments bring higher returns.
The U.S. has been running large trade and budget deficits for years - factors that tend to undermine a country's currency in the long term, unless they are offset by foreigners' willingness to invest money in the United States.