HOUSTON (Reuters) - Saudi Arabia needs "fundamental change," and a public sale of shares in Saudi Aramco, the national oil company, may be part of the solution, former U.S. Secretary of State James Baker said on Tuesday.

Baker, who served under President George H.W. Bush and joined a U.S. delegation to meet Saudi Arabia's new king last year, told a gathering of oil industry dealmakers that changes like the Aramco IPO could help the kingdom address unemployment and budget deficits amid weak oil prices.

"These things are semi-revolutionary ideas, but who's to say they're not what the doctor ordered?" Baker said at a conference hosted by the Association of International Petroleum Negotiators. "There does need to be some fundamental change with the way things are done in Saudi Arabia."

Besides the Aramco IPO, Baker, revered among some Gulf Arabs for his role in orchestrating an alliance against Iraq's Saddam Hussein in the early 1990s, did not specify policies that could bring beneficial change to Saudi Arabia.

Saudi Arabia, the world's largest crude exporter, replaced its energy minister last weekend as part of a major economic shakeup. But industry observers expect the kingdom to continue its "survival-of-the-fittest" strategy aimed at keeping output high to drive higher-cost producers out of the market.

The changes come as Saudi leaders seek to reduce their economy's dependence on oil amid a rout that has caused prices to fall around 60 percent since June 2014. A partial Aramco IPO, which could value the world's largest oil company at more than $2 trillion through the sale of a 5 percent stake, is part of the country's strategy.

"They've got this huge workforce that they can't employ... and of course they're running some substantial budget deficits now," Baker said in a rare public discussion of current Middle East politics.

He added that the kingdom was unlikely to limit production to stabilize prices after members of the Organization of the Petroleum Exporting Countries, along with Russia, failed to agree to a freeze last month.

Baker also criticized Obama's foreign policy, saying Saudi Arabia does not "feel like we have their back anymore" after the nuclear deal with Iran, and said the U.S. should have been "firmer" with Russia after it invaded Crimea in 2014.

"It's not enough to say we may be sliding back into a cold war," said Baker, who was Secretary of State when the Berlin Wall fell in 1989. "We're back."

(Reporting by Luc Cohen; Editing by Dan Grebler and Bernard Orr)