The euro started the week firm at $1.1170 as bulls looked to test the October peak of $1.1179 and the 200-day moving average at $1.1195.
Against a basket of currencies, the dollar was stuck at 97.193 having touched a three-month low at 97.107 on Friday. It was now targeting the August trough of 97.033.
The dollar fared a little better on the yen as safe havens fell from fashion, edging up to 108.23 from Friday's low around 107.87. A holiday in Tokyo made for thin trading.
Sterling remained well bid at $1.2939, after last month's rally from $1.2200, as investors wagered there was less risk of a hard Brexit now that an election campaign was underway.
One of the few movers was the South African rand, which rose as investors were seemingly relieved that Moody's had only downgraded the ratings outlook for the country's debt on Friday and did not cut it to junk as some had feared.
The rand was quoted up about 1% at 14.8650 per dollar, recouping a little of sharp losses suffered last week.
The US dollar itself has been under pressure since the Federal Reserve cut rates last Wednesday and left the door open to more if needed, while all but ruling out the risk of a tightening. "Global policy rates are converging once again at the bottom. That probably means less volatility among currencies as interest rate differentials shrink and the likelihood of any change in policy diminishes," said Marshall Gittler, an analyst at ACLS Global.
"It's also likely to mean a weaker USD, CAD, AUD and NZD as these are the currencies with the highest interest rates currently and therefore the greatest leeway to cut rates. This is probably why USD and CAD were the big losers last week."
Equally, the main gainers last week were the Swedish and Norwegian currencies as interest rates in both countries are seen on hold or even rising in coming months.
Central banks in Australia and the UK hold policy meetings this week and are expected to hold steady, though there is some speculation the Bank of England might drop its tightening bias.
The new head of the European Central Bank (ECB) Christine Lagarde gives her first speech in the role later on Monday and markets assume she will stick with the easy policy script left by Mario Draghi.
There are also at least seven Fed speakers set to speak this week. Investors are also hanging on Sino-US trade talks after both sides said they had made progress toward a Phase-1 deal which might be signed sometime this month.