Vienna, Austria (CNN) -- The United States and other countries agreed Tuesday to resume negotiations with Iran over its nuclear program.
Also Tuesday, Iran signaled a willingness to let international inspectors visit a key military base that international inspectors suspect could be involved in a nuclear weapons program.
The United States, France, Britain, China, Russia and Germany said they would resume stalled talks in a letter from the European Union's foreign policy chief, Catherine Ashton. She was responding to an overture that Iran made last month.
Israel, the United States and other countries have said they suspect Iran is trying to build nuclear weapons. International inspectors also have voiced concern, but Iran insists its nuclear program is for peaceful, civilian purposes.
Israel has spoken openly about the possibility of an attack on Iran's nuclear program.
At a news conference in Washington, President Barack Obama on Tuesday cited the possibility of talks, while stressing the "unprecedented pressure" world leaders have been placing on Iran.
"We're now seeing noises about them returning to the negotiating table," Obama said, adding that it "is deeply in everybody's interests -- the United States, Israel and the world's -- to see if this can be resolved in a peaceful fashion."
Given "the huge toll" Iran is facing from sanctions and isolation, "they understand that the world community means business," he said.
Emphasizing the possibility of a diplomatic solution, the president added, "This notion that somehow we have a choice to make in the next week or two weeks or month or two months is not borne out by the facts."
A top Republican, Senate Minority Leader Mitch McConnell, said Tuesday it "is time to consider a resolution authorizing the use of force." He added, however, that sanctions are useful.
Previous talks with the "P5+1" -- the five permanent members of the U.N. Security Council plus Germany -- broke off in January 2011, when Iran insisted that all U.N. sanctions be lifted and that the other countries agree that Iran has a right to enrich uranium.
Iran's offer and the agreement reached Tuesday suggest that Tehran may no longer require such a condition.
But Iran's state-run news agency IRNA said Tuesday that Ali Asghar Khaji, Iran's deputy foreign minister for Europe and American affairs, had "berated the Western governments for ignoring rules of the game in nuclear talks with Iran" and "expressed hope Western governments would adopt a new approach to Iran based on reality, initiative and renovation of past policies." The report did not make clear what "rules" Khaji was referring to.
"No greater threat exists to the security of Israel and to the entire region -- and indeed the United States -- than a nuclear-armed Iran," U.S. Defense Secretary Leon Panetta said Tuesday to the American Israel Public Affairs Committee, a pro-Israel lobby group. "We want diplomacy to work, we will back the diplomacy with strong and increasing pressure, we will keep all options -- including military action -- on the table to prevent (Iran) from obtaining a nuclear weapon," he added.
Israeli Prime Minister Benjamin Netanyahu discussed Iran on Monday with Obama in Washington.
"Israel must reserve the right to defend itself, and after all, that's the very purpose of the Jewish state: to restore to the Jewish people control over our destiny," he said. "I will never let my people live in the shadow of annihilation."
Obama told the AIPAC group Sunday that "all elements of American power" remain an option to prevent Iran from developing nuclear weapons.
The head of the U.N. nuclear watchdog agency, the International Atomic Energy Agency, said Monday that inspectors wanted to enter Iran's Parchin military base to investigate evidence of ongoing activities there.
Iran offered Tuesday to let international nuclear inspectors in, but only after details are worked out, its team at the IAEA said.
IAEA inspectors had asked to visit the facility during a February trip to Iran but were rebuffed, the agency and Iran have both said.
Iran's permanent mission to the United Nations agency said Tuesday that the IAEA had been out of line to request access to Parchin, but that once the agency formulated an appropriate request, Iran would let inspectors in.
"Considering the fact that it is a military site, granting access is a time-consuming process and cannot be permitted repeatedly," Iran said. Nevertheless, it said it would allow access after the IAEA submits paperwork about "all related issues."
Inspectors say they believe Iran may have used Parchin to test explosives that could be used to detonate a nuclear weapon.
IAEA inspectors visited Parchin twice in 2005, but inspectors did not enter the building that housed the test chamber.
Iran offered access to another site late in the February visit, Amano said. But the inspection team in Iran was not equipped to examine Marivan, a site IAEA officials say may have been used to test elements of a nuclear weapon in 2003.
Iran has said its nuclear program is intended solely for peaceful purposes, but Amano said Iran's failure to cooperate with international inspectors makes it impossible to confirm that that is the case.
In fact, the agency "continues to have serious concerns regarding possible military dimensions" of Iran's nuclear program, IAEA Director General Yukiya Amano said.
Because Iran is not following an agreement to provide expanded information and broader access to international inspectors, the agency is "unable to provide credible assurance about the absence of undeclared nuclear material and activities in Iran, and therefore to conclude that all nuclear material in Iran is in peaceful activities," he said in a statement preceding a news conference.
IAEA inspectors traveled to Iran in January and again in February to discuss the issue, but failed to reach a conclusion, Amano said.
Monday's statement by Amano is not the first time the agency has questioned the purposes of Iran's nuclear program.
Most recently, after the February visit by inspectors, the agency issued a report announcing that Iran had stepped up its efforts to produce enriched uranium in violation of international resolutions and calling on it to stop. In that report, the agency expressed "serious concerns" about potential military uses by Iran.
Among other things, Iran has tripled its monthly production of uranium enriched to contain a 20% concentration of radioactive material and taken other steps to ramp up its nuclear program, Amano said Monday.
While Iran has said the higher-level enrichment is meant to produce therapies for cancer patients and other peaceful purposes, international critics have called the efforts a troubling step toward possible militarization. Nuclear weapons require concentrations of about 90%.
The United Nations, the United States, the European Union and other countries have imposed sanctions related to Iran's nuclear research, and speculation regarding a possible military strike by Israel on Iranian nuclear facilities has been rampant in recent months.
CNN's Antonia Mortensen, Matthew Chance, Reza Sayah, Tom Cohen, Mark Bixler, and Josh Levs contributed to this report.