A top Federal Reserve official said on Friday that the U.S. economy is improving modestly but needs to gather more steam, while inflation remained too low for comfort, underscoring the debate within the central bank over when to scale back stimulus.

"I've been optimistic about the economy and kept projecting that growth is just around the corner, but obviously over the last three quarters growth has averaged only about 1 percent," St. Louis Fed President James Bullard told Reuters.

"So we need to see some indication that growth is going to pick up in the second half before we can be confident things are improving in the way we need."

When it comes to meeting the Fed's growth targets, Bullard said "the arithmetic is getting harder and harder."

In June, Fed Chairman Ben Bernanke detailed plans to start winding down the central bank's monthly bond purchases by the end of the year, provided the economy continues to improve.

But at a meeting this week, the Fed made no mention of slowing bond purchases and instead highlighted the potential risks of modest growth, higher mortgage rates and low inflation.

That was seen by some as a concession to Bullard, who dissented for the first time at the June policy meeting, saying inflation remained too low to justify slowing bond purchases.

Bullard welcomed a slight rise in inflation in the year to July to 1.3 percent, but said it still remains "quite a bit below" the Fed's 2 percent target.

He conceded that the rise "does bolster the (policy-setting Federal Open Market) Committee's story that some of the factors that have held inflation down were temporary and maybe we'll see that come back toward target a little bit."

But he added that "we're going to need more than one month's report to make that conclusion."

Bullard said the overall economy was improving moderately and said a decline in the jobless rate to 7.4 percent in July was good news.

He said job growth has also been "fairly strong" over the last six to nine months, though he called data on Friday showing the economy added a fewer-than-expected 162,000 jobs "a little bit softer."

While the Fed was watching the rise in mortgage rates closely, Bullard said he expected the recovery in housing to remain "pretty strong" with borrowing costs at current levels.

Markets had been prepared for the Fed to start slowing its bond buys as soon as September, though that timeline has been shaken a bit by this week's Fed statement.