Caution prevailed over trade talks between the United States and China. Markets initially welcomed the "Phase 1" trade deal between Washington and Beijing that President Donald Trump outlined last week, but lack of detail kept many investors wary.
"The relief rally for emerging market currencies on the back of the US-China partial trade deal has proven relatively modest so far. The initial price action fits with our own scepticism over whether the trade deal is a game changer for financial markets and the global economy," MUFG analysts said.
A Bloomberg report on Monday, citing sources, said China wants more talks as early as the end of October to decide on the details of the Phase 1 deal before Chinese President Xi Jinping agrees to sign it.
The euro rose as much as 0.2% to $1.046 before giving up most of the gains. Measured against a basket of currencies, the dollar was down at 98.424.
A ZEW economic sentiment indicator is due at 0900 GMT, and should give more insight into euro zone economic confidence.
Elsewhere, sterling rose as much as 0.7% to $1.2699 and 86.90 pence per euro, a five-month high, after Barnier's comments.
China's yuan slipped in offshore markets, a day after reaching a one-month high. The offshore yuan traded at 7.0787 against the dollar, off Monday's high of 7.0503.
The Turkish lira rallied against the dollar after the US announced lighter sanctions than expected following Turkey's invasion of northern Syria. The lira moved away from seven-week lows and was last trading 0.5% higher at 5.897.