"But normalization could become more compelling by the time of the meeting as we get additional information on how the U.S. economy is performing and more information on international and financial market developments, all of which are important in shaping the U.S. economic outlook," he added.
Immediately after Dudley's comments on a September move, stocks spiked, but then pulled back. Additionally, the treasury curve steepened, meaning that traders were betting on a rate hike being put off.
RBS said the futures showed a 20 percent chance of a September hike—the figure stood at 25 percent before Dudley's comments.
Responding to a question about whether a Fed move will come in a subsequent 2015 FOMC meeting, Dudley said he "really" hopes to raise rates this year, but "let's see how the data unfold before we make any statements about exactly when that might occur."
He emphasized that the Fed's decision-making procedure remains data dependent, and said that data points have largely been positive, but "you also have to look at all the other things that could potentially affect the economic outlook."
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"There, international developments and financial market developments do have relevance because they can impinge and affect the economic outlook," he explained.
As for inflation, Dudley said the headline rate remains low because of the drop in oil prices, and the core rate remains flat. But weak oil and a strong dollar will not last "indefinitely," so the he said he expects inflation to rise.
International developments can affect our inflation, he said, pointing to the slowdown in China's growth hurting global commodity prices and emerging market economies. With these events, the dollar strengthens against other currencies, and consumers see effects in the U.S., he said.
Dudley declined to offer a view on why the stock market has suffered in recent sessions, saying that "obviously short-term stock market volatility doesn't really have significant implications for the U.S. economic outlook."
"The stock market really has to move a lot and stay there for it to actually have implications for the U.S. economy," he said, adding that such a move would weigh on the so-called "wealth effect."
Dudley said he hasn't yet seen any effects of the stock drop in economic data, but added that there may be some impact in the University of Michigan consumer confidence numbers next week.
Still, he emphasized that the current turmoil is dissimilar to the financial crisis of 2008 because the genesis of the the crash is abroad, not in the U.S., so "we have to assess" how those international developments could hurt domestic growth.
Responding to a question about the economic slowdown in China, he said Beijing has a challenging task ahead to reorient the economy, but he has faith in the leadership there.
"The good news, though, is that the people there are very capable and they do have quite a bit of resources in terms of what they can do in terms of policy tools to use to help facilitate this transition," he said. "I think I'm reasonably confident in their ability to do so."
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Before the statement on Fed policy, Dudley addressed the health of his region, highlighting New York City's growth.
"While the Great Recession was the deepest and longest recession in modern history for the nation as a whole, New York City bucked that trend to a surprising degree, and did it with little help from Wall Street," he said.
He cited tech companies in the so-called "Silicon Alley," singling out Etsy, as signs of non-finance growth in the city.
Still, he said "pockets of weakness remain" in his region, including Binghamton in upstate New York, which he said "has had no meaningful rebound in employment."
Additionally, the U.S. Virgin Islands and Puerto Rico "remain in a deep economic slump," he said, but employment "appears to have steadied" recently. Puerto Rico's outlook, however, is uncertain given its financial crisis.
—CNBC's Patti Domm and Reuters contributed to this report.