The euro slipped against its most major rivals in the European session on Tuesday, after European Central Bank President Christine Lagarde warned that a second wave of infections across Europe could delay economic recovery from the Covid-19 pandemic.

Speaking to the Wall Street Journal CEO Council, Lagarde said that the containment measures that had to be implemented by authorities would have an impact on the rebound.

"So instead of that V shape that we all long for and hope for, we fear that it might have that second arm of the V a little bit more shaky," she cautioned.

The ECB chief said that the central bank is prepared to use all the tools that will deliver the most effective outcome.

European stocks fell as investors fretted about the impact of a second wave of coronavirus on the economy.

Data from Destatis showed that Germany's factory orders grew at a faster pace in August on robust foreign demand.

Factory orders climbed 4.5 percent month-on-month, which was faster than the 3.3 percent rise in July and the 2.6 percent increase economists' had forecast.

The euro edged down to 124.20 against the yen, 1.0768 against the franc and 1.1765 against the greenback, from its early highs of 124.69 and 1.0790 and a fresh 2-week high of 1.1800, respectively. The next likely support for the euro is seen around 119.5 against the yen, 1.06 against the franc and 1.16 against the greenback.

The euro eased off to 1.5610 against the loonie and 1.7700 against the kiwi, after rising to 1.5646 and a 6-day high of 1.7796, respectively in previous deals. On the downside, 1.52 and 1.74 are possibly seen as its next support levels against the loonie and the kiwi, respectively.

In contrast, the euro recovered to a 4-day high of 0.9092 versus the U.K. currency, from a low of 0.9061 set at 4:45 am ET. The euro is likely to find resistance around the 0.92 mark.

Survey from IHS Markit showed that the UK construction sector registered a sharp expansion in September as new business grew the most since before the pandemic-induced lockdown.

The IHS Markit/Chartered Institute of Procurement & Supply construction Purchasing Managers' Index rose unexpectedly to 56.8 in September from 54.6 in August.

The euro held steady against the aussie, after having risen to a 6-day high of 1.6490, from a low of 1.6363 seen in the previous session. At Monday's close, the pair was worth 1.6308.

Looking ahead, U.S. and Canadian trade data for August will be out in the New York session.

European Central Bank President Christine Lagarde is due to participate in a virtual panel discussion at an event celebrating the 10th anniversary of the European Stability Mechanism at 9:00 am ET.

At 10:40 am ET, Federal Reserve Chair Jerome Powell will deliver a speech about the US economic outlook at the National Association of Business Economics annual meeting, via satellite.