The US dollar could recover in the near term, though, as some traders said the greenback's 3 percent drop so far this month may have been overdone. The slide took the euro to a four-month high against the dollar and the yen to a seven-month high.
The Fed on Thursday said it would pump $40 billion into the economy each month until unemployment falls significantly. The move came a week after the European Central Bank unveiled a new bond-buying program to address the region's debt crisis.
"The outlook for the dollar has definitely been damaged by the policy actions by both central banks -- the Fed and the ECB," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.
The dollar index, which measures the US unit's value against a basket of currencies, stood at 78.919, not far from the 78.601 set on Friday, a level last seen in late February.
The euro was little changed at $1.3120, having hit $1.3169 on Reuters data, the highest since early May and rebounding from a session low of $1.3082.
The common currency has gained 9 percent since hitting a two-year low around $1.2040 in July. Traders said some investors may be tempted to book some profits now, though any pullback could be limited.
"The euro is still likely to move a bit higher. The momentum is not over yet," said Steve Barrow, head of G10 currency research at Standard Bank.
"It may see a dip down toward $1.30 again, but it won't go much below that," he said. "I would be more inclined to buy on dips than to sell on strength."
He also said he expects the euro to rise toward $1.3250-$1.3300 over the next week or so.
The euro on Monday hit an eight-month high against the safe-haven Swiss franc at 1.21849 francs on EBS.
Markets are waiting to see if Spain will ask for help to tackle its debt Crisis. Some analysts said Madrid appeared to be paving the way for formally requesting such assistance after it said it would set clear deadlines for structural reforms by month-end.
The Japanese yen weakened broadly, with the euro rising 0.39 percent to 103.30 yen. The dollar gained 0.41 percent to 78.710 yen, having touched a one-week high of 78.92.
The Japanese government last week lowered its growth outlook for the second month in a row, putting pressure on the central bank to ease monetary policy again, not least to weaken the yen. The Bank of Japan ends a two-day meeting on Wednesday.
The yen was hurt by the downgrade of Japan's economic outlook and "the view that the BOJ's next move could be further quantitative easing," said Michael Woolfolk, senior currency strategist at BNY Mellon in New York.
"After the weekend, traders are beginning to position themselves for what might happen later this week."
Investors are watching how Japanese authorities might respond to the yen's latest rise versus the dollar, sparked by the Fed's action. Market jitters about the potential for yen-selling intervention by Japanese authorities helped limit the dollar's drop last week.