"We must be confident that underlying inflation is moving to our objective, clearly and at sufficient speed. Otherwise, we have work to do," he said in a major speech on Friday in Jackson Hole, Wyoming.
Warsh said that while recent economic data has shown a slight slowdown, he did not see this as indicating any change in the underlying trend.
In an initial reaction to the speech, the euro fell noticeably against the US dollar.
In July, US inflation fell by 0.1 percentage point to 3.4 per cent but the rate has now remained above the Federal Reserve's 2.0 per cent target for more than five years.
This is partly due to the war in Iran and the resulting energy crisis.
"The Fed should therefore prioritise prices at present," Warsh went on to say, describing the inflation rate as "too high".
At the last interest rate decision at the end of July, three of the 12 voting members of the Federal Open Market Committee signalled their openness to an interest rate rise later in the year to curb inflation.
Warsh abstained but reiterated that the Fed would guarantee price stability - an indication that he intends to prioritise the fight against inflation.
The Fed has left the key interest rate unchanged for five consecutive meetings since December 2025, meaning the range remains at 3.5 to 3.75 per cent.
Warsh has said he does not want to provide what analysts call "forward guidance" about whether the Fed will hike or cut rates or stay on hold at upcoming meetings.
He argues that it limits the Fed's flexibility by committing it to a specific policy.
Yet some economists have argued that he could say more about his views on Fed policy without tipping his hand about future actions.
Warsh on Friday reiterated his scepticism about providing such guidance or even outlining his broad approach to interest-rate policy.
But he did suggest that interest rates currently are not restricting economic activity, pointing to robust business investment in artificial intelligence equipment and infrastructure and strong consumer spending.
As a rule of thumb, interest rates often need to be high enough to limit borrowing and spending to cool inflation.
The Fed next meets September 15-16.
with AP
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