On Wednesday, stock investors cheered the Fed's strategy. The Dow Jones industrial average, which had been up about 160 points before the Fed issued its statement, roared higher to close up 280 points. The stock market tends to applaud low rates because they make it easier for individuals and businesses to borrow and spend, and they cause many investors to shift money into stocks in search of higher returns.
Read MoreCramer: Time to tame the oil beast
Energy prices have plunged since the Fed last met in October, with oil hitting a five-year low. That price drop is reducing inflation further below the Fed's 2 percent target, which could heighten the pressure to delay a rate hike until inflation rebounds. On Wednesday, the government said consumer prices rose just 1.3 percent in November compared with 12 months ago.
But Yellen noted that oil price spikes in the past had only temporarily raised inflation and suggested that a corresponding drop will likely also have only a "transitory" effect on inflation.
She was more optimistic about the benefits of lower oil prices for the U.S. economy.
"The decline we have seen ... is likely to be on net a positive," Yellen said. "It's something that's certainly good for families, for households. It's putting more money in their pockets... It's like a tax cut that boosts their spending power."
At the same time, she noted that cheaper oil can undercut wage growth and keep inflation below target.
The Fed's statement was approved on a 7-3 vote. The three dissents reflected the sharp divisions inside the Fed as it transitions from an extended period of ultra-low rates to a period in which it will start to raise rates. The Fed has not raised rates in more than eight years.
The dissents included Presidents Richard Fisher of the Dallas Fed and Charles Plosser of the Philadelphia Fed, who have long stressed the need for the Fed to prevent high inflation. Narayana Kocherlakota, president of the Fed's Minneapolis regional bank, dissented for a different reason: He thinks the Fed should do more to boost inflation to its 2 percent target.
Since the Fed's last meeting, the job market and other sectors of the economy have strengthened. Employers added 321,000 jobs in November, sustaining the healthiest year for job growth since 1999. The 5.8 percent unemployment rate is close to the 5.2 percent to 5.5 percent range that the central bank considers maximum employment.