It nursed those losses on Wednesday, drifting down to 0.9923 Swiss francs, after broaching parity, and falling slightly to 107.64 yen.
The dollar was marginally weaker at $1.0940 per euro and fell against the Australian and New Zealand dollars, retracing some of its large Tuesday gains, while the equities market tumbled.
The Institute for Supply Management had said its index of U.S. factory activity fell to 47.8, the lowest reading since June 2009. A figure below 50 signals the domestic factory sector is contracting.
"While the data... represented a negative surprise in the sense that it came in below consensus expectations, in other ways the industrial slowdown is not a surprise at all," BNY Mellon analysts said in a note, pointing to Sino-U.S. trade tensions and signs of a slowdown around the world.
The manufacturing number is a bad omen for September U.S. labour figures due on Friday, since moves are often correlated, the bank said.
BNY Mellon said that while the Fed "stubbornly" feels rates are appropriate for an economy that continues to perform well, "it will ultimately have to accept that the pillars of support - the labor market and the consumer - are weakening."
Against a basket of currencies the dollar was slightly weaker at 99.087, after hitting a two-year high of 99.667 overnight.
The pound GBP= drifted lower to $1.2296. That has it heading back towards an almost one-month low hit overnight as traders are increasingly nervous about Britain crashing out of the European Union at the end of the month.
Prime Minister Boris Johnson will unveil his final Brexit offer to the European Union on Wednesday and make clear that Britain intends to leave the EU on Oct. 31, no matter what.
The Australian dollar, which hit its lowest in a decade on Tuesday after the Reserve Bank of Australia (RBA) cut interest rates and kept the possibility of further easing alive, bounced a little to $0.6708. But few are expecting a sustained rise.
"A comparison of yesterday's and September's post-meeting RBA statement suggests yesterday's statement is, if anything, slightly more dovish," said Joe Capurso, senior currency strategist at the Commonwealth Bank of Australia in Sydney.
"We expect the RBA to cut the cash rate again in February 2020," he said.
Trading could be subdued in Asia on Wednesday time because China's financial markets are closed until Monday for public holidays. In offshore trade, the Chinese yuan was steady at 7.1448 per dollar.
(Reporting by Tom Westbrook; Editing by Richard Borsuk) ((firstname.lastname@example.org; +65 6318 4876;))