The euro touched a four-month high versus the dollar in the wake of the Fed action. Some traders and analysts said the euro could add to its gains in the near term, although a sharp rise seemed unlikely.
But in the wake of its recent rally, the euro's scope for further gains against the dollar may be limited, noted Akira Hoshino, chief manager for Bank of Tokyo-Mitsubishi UFJ in Tokyo.
"I don't get the sense that it will keep on going. A slight break above $1.30 might be all that it can manage," Hoshino said.
The euro climbed to as high as $1.3016 on trading platform EBS, its highest level in four months, and last stood at $1.3008 , up 0.2 percent from late US trade on Thursday.
While the risks of an extreme crisis in the euro zone seem to have receded for now, a continued rise in the euro could be negative for the euro zone's economy and that is one reason to be cautious about the single currency's outlook, said Hoshino at Bank of Tokyo-Mitsubishi UFJ.
"With backstops in place, the chances of scenarios such as a breakup of the euro or a Greek exit seem to have declined to some extent," he said.
"But at the same time, persistent euro strength is something that would be negative for Europe," Hoshino said, adding that European officials may not be too happy about the euro's recent sharp rise.
The dollar index, which measures the dollar's value against a basket of currencies, fell to 79.134, its lowest level since early May.
JAPAN IN A BIND
In fresh efforts to stimulate growth, the Fed said on Thursday it would buy $40 billion of mortgage-backed debt per month until the outlook for jobs improved substantially. It also expects interest rates to stay near zero until at least mid-2015, even if the economy recovers.
Traders and analysts said the Fed's bold action had put in a bind by lifting the yen to levels that threaten already sluggish exports.
The drop in the dollar has the market jittery about the potential for yen-selling intervention, said Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation in Singapore.
"On the face of it, you would expect the dollar to be sold (versus the yen). But if I were a dealer, I don't think I would be able to sell from here," Okagawa said.
Adding to the anxiety, traders said the Bank of Japan, which conducts currency intervention on behalf of Japan's finance ministry, had conducted a rate check on Thursday after the Fed's decision.
Such rate checks are regarded by traders as a sign that Japanese authorities may be moving closer to conducting actual intervention.
The dollar edged up 0.1 percent to 77.56 yen, stuck near a seven-month low of 77.13 yen set on Thursday.