The risk of the Fed missing its 2% inflation target and the trade war were two key macroeconomic challenges to the policy-setting Federal Open Market Committee (FOMC), he said in a presentation prepared for an audience at the Foreign Correspondents' Club (FCC) in Hong Kong.
The Fed held interest rates steady earlier in May, when Chairman Jerome Powell said there was "no strong case" for either a cut or hike in interest rates.
But Bullard said on Wednesday "a downward policy rate adjustment even with relatively good real economic performance may help maintain the credibility of the FOMC's inflation target going forward."
"A policy rate move of this sort may become a more attractive option if inflation data continue to disappoint," he said.
Bullard and Chicago Fed's Charles Evans, both voting members of the FOMC, have in recent days expressed concerns over the Fed's failure to meet its target. Bullard said on Wednesday that another 'low-side miss' is on the horizon in 2019.
Bullard said any policy adjustment going forward would be in response to incoming data, and not a continuation of the rate normalisation process which has stopped earlier this year after 225 basis points worth of hikes from near zero levels.
He remained upbeat about growth prospects.
Bullard drew comparisons with 2-1/2 decades ago -- when rates were increased by 300 basis points between early 1994 and early 1995, and the economy still boomed during the second half of the 1990s -- to stress that rate normalisation can be accomplished without damaging prospects for an extended period of growth.
The next FOMC meeting will convene on June 18. [FED/DIARY]
Bullard expects agreements on trade will be reached in the near term, but warned that a failure to do so, with substantial barriers "erected and maintained," could alter "global trading patterns over the medium term".
These unresolved trade disputes and the below-target inflation "suggest that the FOMC needs to tread carefully in order to help sustain the economic expansion," he said.
Bullard said that from a macroeconomic perspective, China should agree to "everything that's being asked" in the negotiations because it would lead to a domestic economic boom.
"They will establish credibility on trade inside China, and will reassure foreign investors that they can invest in China and be treated appropriately. If that occurs, I would see blue skies ahead for the Chinese economy," Bullard said.
"It's not just the U.S. that's doubting Chinese credibility. Many global players all around the world have found that it's a difficult place to do business."
In an interview with Bloomberg TV earlier on Wednesday, Bullard said tariffs would have to stay on for "something like six months" with no prospect of a resolution in sight to weigh on Fed policy.
In his FCC remarks, he added China selling its large stock of U.S. Treasuries was not "as big of a threat as it's being made out to be" as it would be hard to replace them with other assets.
(Editing by Jacqueline Wong)
By Noah Sin and Marius Zaharia