WASHINGTON (Reuters) - Policymaking members of the Federal Reserve worried inflation pressures were mounting when they last met in March, and wondered whether they would need to raise rates more than thought to control it.

"Many participants indicated that their uncertainty about the intensity of inflation pressures had risen...and that, in particular the distribution of possible inflation outcomes, was now tilted a little to the upside," according to minutes from the March 22 meeting of the Federal Open Market Committee released Tuesday.

While policy-makers thought inflation likely will be contained, they felt that rates might have to keep moving higher for a longer period to ensure that outcome.

"Although the required amount of cumulative tightening may have increased, members noted that an accelerated pace of policy tightening did not appear necessary at this time," the minutes said.

The Fed minutes were a relief for financial markets, on edge over the possibility the U.S. central bank might be on the verge of bigger rate rises of half percentage points that would be more disruptive to investors.

On Wall Street, stock and bond prices rallied as investors worried about inflation -- and possible more agressive rate hikes from the Fed -- breathed a sigh of relief.

For more on the market reaction, click here. To check whether investors might be overdoing it, click here.

There were signs that FOMC members had argued whether it was time to change the structure of their closely-scrutinized statement issued after each policy session, with some urging the panel to drop its assessment of risks faced by the economy.

"A number of members believed that formulaic language by its nature was too rigid to reflect evolving economic circumstances in a satisfactory manner, especially when developments were subtle or complex, and some of these members believed that the risk assessment should be discontinued," the minutes said.

While there was also concern that a commitment to a "measured pace" of rate rises was a potential restraint on policy, Fed members agreed they were not constrained by it, should they need to act more decisively on rates.

The FOMC members "believed that the wording did not rule out either picking up the pace or pausing in the process of removing policy accommodation should circumstances warrant."

The Fed has now moved its trendsetting federal funds rate up steadily in seven successive quarter percentage point increments to 2.75 percent.

In the process, "measured pace" has come to be associated with rises of a quarter point, which the minutes said created "some discomfort" because it seemed to be so explicit about Fed intentions.

In the end, the policymakers decided their statement "would need to evolve over time," but left it unclear how that will happen.

Analysts said the minutes imply a debate within the Fed about whether its policy is well attuned to keeping inflation risks under control.

"Clearly there is a debate about whether they need to turn more aggressive," said economist Steve Gallagher of SG Corporate & Investment Banking in New York, but no clear-cut conclusion.

In fact, several analysts thought the minutes implied that, while it might be on heightened watch, the Fed was prepared to continue with modest rate rises.

"This reiterates the view of many that a quarter point per meeting for the rest of this year is in the cards," said Tim Mazanec, director of foreign exchange at Investors Bank and Trust Company in Boston.

Indeed, the Fed cited several reasons for hope that recent sources of inflation risk will diminish. "One source of upward pressure on inflation had been the rise in energy prices, and it seemed reasonable to expect that those prices would level out or even decline mildly, as built into futures prices," the minutes said.

In addition, while slack in labor markets was "gradually diminishing," rising rates of productivity or hourly output per worker were a damper on wage demands and were keeping inflation from this source muted, the minutes said.

Read about the Fed minutes' affect on stocks.