The euro was last at $1.1060, not far from a two-week low of $1.1042 touched in the previous session.
The yen fell to $147.10 in early trade, close to a two-week low of $147.16 hit on Monday.
Investors will focus this week on U.S. jobs data due on Friday after Federal Reserve Chairman Jerome Powell last month backed the imminent start of interest rate cuts, citing concerns about the labor market.
Before that, the job openings data will be released on Wednesday and the unemployment claims report on Thursday, which will be in the spotlight.
The CME Group’s FedWatch tool showed markets are pricing in a 69 percent chance of a 25 basis point rate cut when the Fed meets on Sept. 17-18, with a 31 percent chance of a 50 basis point cut.
According to Reuters, the dollar index, which measures the performance of the US currency against six major currencies, fell to 101.69 in early trading, which is slightly below the highest level in two weeks at 101.79 that it touched yesterday, Monday.
The index fell 2.2 percent in August amid expectations of a U.S. interest rate cut.
The pound was down slightly at $1.31425 in early trade. The Australian dollar fell 0.14 percent to $0.6782, while the New Zealand dollar fell 0.18 percent to $0.6223.
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