(Reuters) - San Francisco Federal Reserve Bank President Mary Daly on Friday said the decision by the U.S. central bank to lower interest rates on Wednesday by another quarter percentage point was a "close call," adding she agreed with Chair Jerome Powell that caution is now warranted toward further policy adjustments.

"The most important thing to me was we needed to recalibrate policy. I saw this as a close call," Daly said in an interview with Bloomberg TV. "Now I feel we have the recalibration phase behind us, and we're in the next phase, and that next phase is really looking at the incoming information."

Daly's remarks were the first by a U.S. central banker since the Fed on Wednesday cut its policy rate to a range of 4.25% to 4.50%, with officials updating projections showing most see fewer cuts in 2025 than they had projected previously.

The new median estimate for the appropriate level of the Fed funds rate by the end of next year was 3.9% - or a range of 3.75% to 4.0% - up from an earlier projection of 3.4% - or a range of 3.25% to 3.50%.

Daly said she was comfortable with that more moderate path of easing shown in the summary of economic projections.

"I was very comfortable with that median," she said. That makes sense to me, but we have to remain agile."

Following Powell's press conference on Wednesday - and his repeated references to taking a "cautious" approach from here - rate futures markets have repositioned and now show doubt within the market about whether the Fed will deliver the two quarter percentage point cuts in 2025.

"We might end up with fewer cuts than two," Daly said. "We might have to respond and end up with more if inflation falls faster or you see a significant weakening in the labor market. And I'm comfortable sitting in that center court position and waiting for the data to come in, and we'll actually respond as they do."

(Reporting By Dan Burns; Editing by Ros Russell)