In his inaugural address, President Barack Obama signaled conciliation to America’s foes by using the metaphor of an outstretched hand to an unclenched fist.

Already, there are signs that some of those foes were listening, sensing an opening for improved relations after eight combative years under President George W. Bush. Fidel Castro is said to like the new American leader, and North Korea and Iran both sounded open to new ideas to defuse nuclear-tinged tensions.

Unclear is what they will demand in return from the untested American statesman, and whether they will agree to the compromises the U.S. is likely to insist on in exchange for warmer relations.

Are the Castro brothers really willing to move toward democracy? Can Russia and the West heal their widening estrangement? Will Venezuelan President Hugo Chavez stop being a thorn in America’s side?

Analysts say they see many bright opportunities amid the perils and complexities.

“In this dangerous world, in a world where America’s leverage has either been exposed as not being as strong as the rhetoric implied or where it is simply diminishing, I think Obama’s approach is exactly what America needs,” said Robin Niblett, the director of Chatham House, the London-based think tank.

Nowhere are the opportunities — and the risks — of diplomacy more stark than in the Middle East.

Iran still considers the U.S. the “Great Satan,” but a day after Obama was sworn in, it said it was “ready for new approaches by the United States.” Foreign Minister Manouchehr Mottaki said his country would study the idea of allowing the U.S. to open a diplomatic office in Tehran, the first since the 1979 Islamic Revolution.

Still, the differences between the two nations are deep — U.S. suspicions about Iran’s nuclear program, President Mahmoud Ahmadinejad’s threats to annihilate Israel, and Tehran’s support for militants in Iraq — and analysts say that baby steps are all that can be hoped for, at least in the short term.

Iran’s parliament speaker, Ali Larijani, said the country had doubts that Obama’s Mideast policy will be different from the Bush administration, state television reported Sunday.

And diplomacy has its limits: Some experts feel the Islamic nation is committed to developing nuclear weapons, whatever the cost.

Obama may think “he can convince Iran to give up its nuclear program, but this is a red line for Iran,” said Saudi political analyst Khaled al-Dakhil.

Israel and the Palestinians present the new president with one of his greatest challenges, and he has been quick to demonstrate his interest.

With the latest Gaza fighting still reverberating around the world, Obama appointed George Mitchell, mediator of peace in Northern Ireland, as special envoy to the Middle East.

While the task is daunting, some see room for Obama to maneuver.

Syria, which has teetered between pariah and potential peace partner, has indicated that it seeks no further quarrel with Washington, even saying it would like the new administration to mediate stalled Syrian-Israeli peace talks.

If Obama helps Syria in from the cold, analysts say it could have far-reaching benefits. Syria has great influence over two of Israel’s main enemies — Hezbollah in neighboring Lebanon, and Hamas, whose leaders live in Damascus. Assad could also help pressure Syrian ally Iran to take a more measured stance.