Republicans, and have taken a hard line, speaking openly about a possible military strike in Iran, even as they say they support diplomatic measures to persuade the country to abandon its nuclear ambitions.
Democrats say they favor multinational diplomacy, combined with economic incentives as well as sanctions. They've repeatedly criticized President Bush for refusing to negotiate with Iran, and say they would consider military action only after exhausting other options.
Among themselves, they've turned the question into a proxy battle between front-runnerand her rivals over issues of foreign policy experience, judgment and leadership.
Rand Beers, who has worked as a national security adviser to both Republican and Democratic presidents, sees a subtext to all the rhetoric.
"For Republicans, Iran represents a much more comfortable foreign policy subject to talk about than Iraq. It's a hard-nosed, hawkish credentialing and branding issue," Beers said. "On the Democratic side, there is far less saber rattling. They are trying to distinguish themselves from Bush and promote a dialogue and find common ground with Iran, which there may not be."
There is little doubt that relations between Iran and the U.S. have reached a toxic and potentially dangerous level - a situation the next president is likely to inherit in some fashion.
Iran has refused to back down on its nuclear aspirations, saying it seeks electricity, not weapons. According to the U.S. government, it also has sponsored terrorism throughout the Middle East and continues to support Shiite militias in Iraq that have been involved in attacking American soldiers.
The Bush administration last week slapped tough new sanctions on Iran, and the president recently warned that a nuclear Iran could lead to World War III.
That kind of rhetoric has been echoed and amplified in the GOP presidential contest.
Former New York Mayor Giuliani, former Tennessee Sen. Thompson and former Massachusetts Gov. Romney have spoken of a willingness to take pre-emptive military action against Iran if necessary. Giuliani has been especially vocal, promising a strike if Iran develops a weapon during his presidency.
Romney last month proposed indicting Iran's president, Mahmoud Ahmadinejad, on a charge of inciting genocide.
, the Arizona senator and Vietnam War hero, has been somewhat less bellicose. But he told The Associated Press that "there's only one thing worse than military action against Iran and that is a nuclear-armed Iran."
Clinton's vote in favor of a Senate measure designating Iran's Revolutionary Guard a terrorist group has made her a target of stinging criticism from several Democratic rivals. That vote is expected to be a major point of contention Tuesday when the candidates meet in a two-hour debate in Philadelphia.
Fellow Sen.of Illinois and former Sen. of North Carolina say Mr. Bush could interpret the measure as congressional approval for a military attack. Clinton has vigorously denied that would be the result and says she was voting for stepped-up diplomacy and economic sanctions.
For her part, Clinton contends that comments by Obama on personal diplomacy with countries like Iran are evidence that the Illinois senator is too inexperienced to lead in a dangerous world.
In a July debate, Obama was asked if he would be willing to meet, without precondition, the leaders of Iran and other unfriendly nations during the first year of his presidency. He replied, "I would."
Clinton said that showed Obama was "irresponsible" and "naive" on foreign policy matters. The former first lady, now a New York senator, has called for more direct diplomacy with Iran and countries such as North Korea, but has also said she would not commit to leader-to-leader meetings.
In New Hampshire on Monday, Giuliani mocked the Democrats' entire discussion of Iran, suggesting the top candidates are too eager to negotiate.
"This is the world we live in. It's not this happy, romantic-like world where we'll negotiate with this one, or we'll negotiate with that one and there will be no preconditions, and we'll invite Ahmadinejad to the White House, we'll invite Osama to the White House," Giuliani said.
"Hillary and Obama are kind of debating whether to invite them to the inauguration or the inaugural ball," he added.
Paul Pillar, a professor of security studies at Georgetown University, said candidates on both sides could do a better job speaking responsibly about the complex problem of Iran.
"The campaign rhetoric hasn't been particularly illuminating on this issue," Pillar said. "On the Democratic side, there has been too much silliness on the issue of engagement, and a candidate's particular choice of words for conditions for talking. The rhetoric on the Republican side ignores a bunch of important questions - the Iranian response, our standing in the region and around the world, and poisoning relations with Iran for generations to come."