"EUR/USD seems to be comfortably trading around its new lows and in the next few days we expect to see a continuation in the recent downtrend rather than any clear rebound," said ING analysts.
"The fears around the coronavirus impact on the Eurozone economy remain well in place while data this week should be in line with latest releases in providing a non-encouraging picture."
The euro nudged higher to $1.0845 in early trading but had earlier touched $1.0817, its weakest since mid-2017.
The currency has lost 2.3% of its value against the dollar so far in February.
Kit Juckes, an analyst at Societe Generale, said that while data shows that the market is building a short euro position, "it remains a long way from its peaks".
It was a quiet start to the week elsewhere, with much of the United States off for a public holiday.
The yen was unfazed by weak economic growth data in Japan. It traded down 0.1% at 109.84 yen per dollar JPY=EBS .
Japan, the world's third-largest economy, shrank 1.6% in the three months to December, the largest drop in six years, hit by a sales tax hike.
With growth faltering in the euro zone and Japan, most market players expect the U.S. economy to remain stronger among its developed world peers, although retail sales and industrial production numbers on Friday were disappointing.
The dollar index stood at 99.095, near Friday's 4-1/2-month high of 99.241.
The Australian dollar strengthened as investors assessed the latest reading on the coronavirus in China, where the number of cases rose but new deaths dropped.
The Australian dollar, used as a proxy for risk on Chinese assets, rose 0.1% to $0.6724. The currency has partly been supported by expectations of stimulus from Beijing.
The offshore Chinese yuan gained 0.2% to 6.9815 per dollar.
Some analysts think the market may be underestimating the hit from the coronavirus on both China's economy and on growth in the rest of the world, especially Asia.
"For China, our new base case is 3.0% GDP growth in Q1, with the risk firmly skewed to an even lower number - too much damage has already been done and initial policy stimulus will not be very effective," Nomura strategists said in a research note.
Sterling slipped 0.2% to $1.3015 , reversing some of its gains last week when the appointment of a new British finance minister raised expectations that the government would significantly lift public spending in next month's budget.
(Reporting by Tommy Reggiori Wilkes Editing by William Maclean and Gareth Jones) ((email@example.com))