NEW YORK (Reuters) - Former Federal Reserve Chairman Alan Greenspan said the probability of a US recession was now slightly more than a third, after he earlier in the year put the chances at one-third, The Wall Street Journal reported in its online edition on Monday.

Greenspan said there was a "very large" inventory of unsold, newly built homes putting pressure on builders to sell them quickly, the Journal reported, citing an interview with him.

As a result, "we have the capability of far bigger price declines," which will pinch home equity, lead to more defaults on subprime mortgages and pressure consumer spending, Greenspan said, according to the Journal.

Greenspan, who stepped down as chairman of the Fed in January 2006 after more than 18 years at the helm of the U.S. central bank, is giving interviews to promote his memoir, "The Age of Turbulence: Adventures in a New World," which is being published on Monday.

In the Journal interview, Greenspan said he had put the odds of a national decline in housing prices at less than 50-50, at least until a couple of months ago, based largely on the experience of Britain and Australia.

But he said he had become less optimistic since his book was finished, when it became clear the construction industry was unable to cut the number of housing starts below the rapidly falling level of home sales, the Journal reported.

Greenspan also expressed dismay in the Journal at the Democratic Party. In his book, he criticizes President George W. Bush and congressional Republicans for abandoning fiscal discipline and putting politics ahead of sound economics.

Greenspan told the Journal he was "fairly close" to former President Bill Clinton's economic advisers, but, "the next administration may have the Clinton administration name but the Democratic Party ... has moved ... very significantly in the wrong direction." He cited its populist bent, especially its skepticism of free trade. Clinton's wife, Sen. Hillary Clinton, is the Democratic presidential front-runner.

Greenspan, a self-described libertarian Republican, said he was not sure how he would vote in the 2008 election, the Journal said.

"I just may not vote," the Journal quoted him as saying.

"I'm saddened by the whole political process, and it's not an accident that Republicans deserved to lose (congressional elections) in 2006 -- it wasn't that the Democrats deserved to win," the Journal quoted Greenspan as saying. "When it came time to rule, all of a sudden their ratings collapsed, and the reason they collapsed is they're just as negative as the Republicans."

(Reporting by Lewis Krauskopf)