Mr Greenspan is likely to hold rates steady
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The US central bank, the Federal Reserve, has decided to keep interest rates at a 45-year low of 1%.
The Federal Open Markets Committee (FOMC), under chairman Alan Greenspan, has cut rates 13 times since early 2001 in an effort to kick-start economic expansion.
But the Fed is now expected to keep rates at their current level for some time, in the hope of making sure the recovery takes hold.
In a statement, the Fed said low rates could can be maintained "for a considerable period".
Deflation risk
The Fed's statement was nearly identical to one issued with the last rate decision a month ago, with the committee saying it saw "the upside and downside risks" to the economy as "roughly equal".
The committee also repeated its warning about the slight risk of deflation, which was significant enough to maintain low rates.
"The probability, though minor, of an unwelcome fall in inflation exceeds that of a rise in inflation from its already low level," the panel said.
Its assessment was backed by the latest US inflation figures, released earlier on Tuesday, which were slightly lower than predicted.
"The prospect of deflation is very scary," Dunvegan Associates chief investment strategist AC Moore told BBC World Business Report.
Widely expected
The Fed's decision was widely expected on Wall Street and had little impact on a rising market.
The Fed "did exactly what we all thought they would do", said Edgar Peters, chief investment officer at PanAgora Asset Management in Boston.
"They come right out and said that monetary policy can be accommodative for a long time, and it seems like that's what they intend to do.
"Everything was as expected, and because of that, the market's not reacting."
Inflation figures
One change, however, was in the Fed's attitude to the labour market, which is worrying many economists.
Even though growth is picking up, the "jobless recovery" is still bleeding jobs according to recent figures, with almost 3 million gone in the past two and a half years.
"The Fed had described the labour market indicators are mixed and this statement describes the labour market as weakening, so it's a touch more dovish," said Henry Wilmore, chief economist at Barclays Capital, New York.
The Dow Jones industrial average was up 54 points, or 0.47%, at 9,502.84, after briefly dropping to 9,485 and then recovering above the 9,500 mark in the first few minutes after the Fed's announcement.
Earlier, the broadest measure of US consumer prices rose 0.3% in August to stand 2.2% higher than one year ago, while so-called "core" inflation - which strips out volatile food and energy prices - inched 0.1% higher.
Economists had forecast that broad consumer prices would rise 0.4%, while core inflation would climb 0.2%.
The annual rate of core inflation now stands at just 1.3%, its lowest level in 37 years.