President Obama’s credibility problem has battered his approval ratings, complicated his relationship with foreign allies and harmed his party’s prospects in next year’s midterm elections.

But the decline in the public’s opinion of his trustworthiness presents a particular set of challenges for his diplomacy with Iran, highlighted this weekend by an agreement that will temporarily freeze the country’s nuclear program in exchange for limited sanctions relief.

Some of those challenges are arising now, reflecting mostly partisan opposition to a deal struck by a politically fragile president. But those obstacles are relatively easy to manage — either with the bully pulpit or the veto pen.

The more serious concerns will come in six months, when the negotiated freeze will end with either Iranian pledges to begin dismantling its enrichment capacity or in stalemate.

As Obama told supporters in San Francisco on Monday: “If Iran seizes this opportunity and chooses to join the global community, then we can begin to chip away at the mistrust that’s existed for many, many years.”

For U.S. allies such as Israel and Saudi Arabia who will likely never trust Iran, Obama’s credibility will matter even more.

Will Obama — eager for a legacy-shaping foreign policy achievement — end talks he celebrated as “a new path toward a world that is more secure?” Or will he allow Iran more time — freezing in place what Israeli officials and others say is an advanced uranium enrichment program?

Abandoning negotiations or restoring sanctions would mark a step toward war amid rising isolationism at home and just months before the official conclusion of the United States’ long conflict in Afghanistan.

Any decision will likely take into account his standing at the time — whether immigration reform is advancing in Congress, if his health-care law is functioning, and if his promised limits on National Security Agency eavesdropping practices have appeased his allies abroad and at home.

Even some allies are not convinced that Obama would abandon a process he has spent so much time, diplomatic energy and political capital developing. He told the U.N. General Assembly this year that corralling Iran’s nuclear program was a top priority for his remaining time in office.

Some allies fear that only an egregious Iranian breach of the interim agreement would be enough to dissuade Obama from continuing negotiations. Such a provocation is unlikely to come from a country shrewd enough to steadily advance a nuclear program for more than a decade despite broad international opposition, critics say.

“Obama will not pay a price in the polls for, let’s say, not intervening in Syria,” said a Western diplomat allied with the United States. “He will pay a price in the polls if he gets America into another Middle East war.”

Obama campaigned in favor of talking to the Islamic republic in 2008, enduring accusations of foreign policy naivete for doing so. Succeeding now would have a special I-told-you-so resonance for Obama, and would give him a foreign policy success that eluded his more hawkish predecessor.

A Washington Post-ABC News poll earlier this month found that 64 percent of Americans support rolling back economic sanctions in exchange for Iran’s acceptance of limits on its nuclear program.

But trust in Obama is a key factor in that support. Of those who said Obama is honest and trustworthy, 72 percent back the principles of the agreement with Iran. Support drops by 16 percentage points among those who say they do not trust the president.

Trust is also an essential ingredient of the U.S.-Israel relationship and the U.S.-Saudi relationship. Both have suffered at times under Obama.

The royal family in Riyadh was jolted by Obama’s decision in early 2011 to end support for Egyptian President Hosni Mubarak amid rising public demonstrations. Saudi diplomats concluded that if the Saudi ruling elite faced public unrest, Obama would abandon them, too.

The word “crisis” has often been applied to Obama’s relationship with Israel and its leader, Benjamin Netanyahu, who declared the Iran agreement a “historic mistake.” But according to close observers of the relationship, only three episodes in the rocky Obama-Netanyahu partnership have risen to true crisis level.

They include Israel’s announcement of new settlement construction during Vice President Biden’s March 2010 visit; Obama’s citing the pre-1967 boundaries as negotiating parameters without consulting Israelis; and Netanyahu’s apparent preference last year for Mitt Romney’s candidacy for president.

Diplomats involved in the Iran negotiating process say that Netanyahu, while preferring an interim deal that would have begun dismantling Iran’s enrichment capabilities, still trusts Obama to prevent the country from developing a nuclear weapon.

Hours after the agreement was reached, Obama warned that “if Iran does not fully meet its commitments during this six-month phase, we will turn off the relief and ratchet up the pressure.”

The worry for Netanyahu is: What if Iran meets its commitments but does nothing else to roll back a nuclear program it has spent tens of billions of dollars developing? Can Obama be trusted to end the process and move to a war footing?

Those are the unanswered questions at the heart of Netanyahu’s criticism that the deal has made the world “a much more dangerous place.”

Obama will have an easier time explaining the agreement and the reasons behind it to a domestic audience.

Avoiding wars and caring for those who have fought them are Obama priorities shared by much of the country.

In his statement after the agreement was signed, Obama asked Congress not to impose new economic sanctions against Iran during the six-month pause.

He would be able to veto a sanctions measure, assuming he could keep enough Senate Democrats on his side. That will be harder to do if, after six months, no progress has been made on the agreement’s next stage.

“Tough talk and bluster may be the easy thing to do politically,” Obama said Monday in San Francisco, “but it’s not the right thing for our security.”

Scott Clement, a survey research analyst for Capital Insight, the independent polling group of Washington Post Media, contributed to this report.