WASHINGTON (AP) — The U.S. and Iran stepped back from the brink of possible war Wednesday, as President Donald Trump indicated he would not respond militarily after no one was harmed in Iran's missile strikes on two Iraqi bases housing U.S. troops.

Speaking from the White House, Trump seemed intent on deescalating the crisis, which reached a new height after he authorized the targeted killing last week of Gen. Qassem Soleimani, the head of Iran's elite Quds Force. Iran retaliated overnight with its most direct assault on America since the 1979 seizing of the U.S. Embassy in Tehran, firing more than a dozen missiles from its territory at the installations in Iraq.

Trump credited an early warning system "that worked very well" for the fact that no Americans or Iraqis were killed. He added that Americans should be "extremely grateful and happy" with the outcome.

Trump, facing one of the greatest tests of his presidency, said Wednesday that Iran appeared to be "standing down" and said the U.S. response would be to put in place new economic sanctions "until Iran changes its behavior."

The strikes had  pushed Tehran and Washington perilously close to all-out conflict and put the world's attention on Trump as he weighed whether to respond with more military force. The Republican president delivered his remarks surrounded by his national security advisers in the foyer of the White House. His comments came after a late-night tweet in which he insisted "All is well!" after the strikes.

Despite the conciliatory talk, the region remained on edge Wednesday. Americans forces, including a quick reaction force dispatched over the weekend, remained on high alert. The conflict could still play out in unpredictable ways in the weeks and months to come, with Tehran's proxies in the region able to carry out attacks. And there was no obvious route toward a rebooting of diplomatic engagement, as Trump pledged to ratchet up the "maximum pressure" campaign of economic sanctions that helped bring on the recent escalation.

Iran, for days, had promised to respond forcefully to Soleimani's killing, but its limited strike on two bases — one in the northern Iraqi city in Irbil and the other at Ain al-Asad in western Iraq — appeared to signal that it was also uninterested in a wider clash with the U.S. Foreign Minister Mohammad Javad Zarif tweeted that the country had "concluded proportionate measures in self-defense."

Trump, who is facing reelection in November, campaigned for president on a promise to keep the United States from engaging in "endless war."

On Wednesday he said the United States is "ready to embrace peace with all who seek it." That marked a change in tone from his Tuesday warning, "If Iran does anything that they shouldn't be doing, they're going to be suffering the consequences, and very strongly."

Trump opened his remarks by reiterating his promise that "Iran will never be allowed to have a nuclear weapon," even as that country announced in the wake of Soleimani's killing that it would no longer comply with any of the 2015 nuclear agreement's limits on enrichment that had been put in place to prevent it from building a nuclear device.

He seized on the moment of calm to call for new negotiations to replace the deal from which he withdrew the U.S., objecting that it didn't limit Iran's ballistic missile programs or constrain its regional proxy campaigns like those led by Soleimani.

The president spoke directly to Iran, saying, "We want you to have a future and a great future."

Trump also announced he would ask NATO to become "much more involved in the Middle East process." While he has frequently criticized NATO as obsolete and has encouraged participants to increase their military spending, Trump has sought to have the military alliance refocus its efforts on modern threats.

Like U.S. troops in the region, NATO forces have temporarily halted their training of Iraqi forces and their counter-Islamic State efforts, and re-positioned some forces due to the current instability.

Iran's Supreme Leader Ayatollah Ali Khamenei, speaking on Wednesday, said the overnight strike was not necessarily the totality of Iran's response.

"Last night they received a slap," Khamenei said. "These military actions are not sufficient (for revenge). What is important is that the corrupt presence of America in this region comes to an end."

Soleimani's death last week in an American drone strike in Baghdad prompted angry calls for vengeance and drew massive crowds of Iranians to the streets to mourn him. Khamenei himself  wept at the funeral in a sign of his bond with the commander.

The Iranians fired a total of 15 missiles in the latest strikes, two U.S. officials said. Ten hit the Ain al-Asad air base in Iraq's western Anbar province and one targeted a base in Irbil in Iraq's semi-autonomous Kurdish region. Four failed, said the officials, who were not authorized to speak publicly about a military operation.

U.S. defense officials said American early warning systems detected an incoming ballistic missile well in advance, providing U.S. and coalition forces adequate time to take shelter at both bases.  Officials also said that the U.S. was aware of preparations for the attack. It's unclear if any intelligence identified specific targets or was more general.

Ain al-Asad was first used by American forces after the 2003 U.S.-led invasion that toppled dictator Saddam Hussein, and it later was used by American troops in the fight against the Islamic State group. It houses about 1,500 U.S. and coalition forces. Trump visited it in December 2018, making his first presidential visit to troops in the region. Vice President Mike Pence visited both Ain al-Asad and Irbil in November.

Trump spoke of new sanctions on Iran, but it was not immediately clear what those would be. The primary agencies involved in implementing such penalties – the departments of Commerce, State and Treasury – do not preview those actions to prevent the targets from taking steps to evade them.

Since withdrawing from the 2015 nuclear deal, the administration has already imposed harsh sanctions on nearly every significant portion of Iran's economic, energy, shipping and military sectors.

The effort to deescalate the conflict comes after world leaders, including Turkish President Recep Tayyip Erdogan and Russian President Vladimir Putin, appealed to both sides for restraint.

The fallout for Trump's order to kill Soleimani had been swift.

Iraq's Parliament voted to expel U.S. troops from Iraq, which would undermine efforts to fight Islamic State militants in the region and would strengthen Iran's influence in the Mideast.

The counterattack by Iran came as Trump and his top advisers were under pressure to disclose more details about the intelligence that led to the American strike that killed Soleimani.

Top Senate Democrats, citing "deep concern" about the lack of information coming from the Trump administration about the Iran operation, called on Defense Department officials to provide "regular briefings and documents" to Congress.

Minority Leader Chuck Schumer and the senators also registered their "grave concern" with Trump's comments on targeting Iranian cultural sites and asked for clarification.

Members of Congress were being briefed on the strike Wednesday afternoon in closed-door sessions on Capitol Hill.

Trump and top national security officials have justified the airstrike with general statements about the threat posed by Soleimani, who commanded proxy forces outside Iran and was responsible for the deaths of American troops in Iraq.

One lawmaker who has read the classified notification that Trump sent Congress after the U.S. air strike that killed Soleimani said the two-page document did not describe any imminent planned attacks or contain any new information. The lawmaker, who spoke on condition of anonymity to describe the classified document, said the letter gave a historic account of attacks that have been reported publicly.

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Associated Press writers Deb Riechmann, Robert Burns, Kevin Freking, Lolita Baldor, Darlene Superville, Alan Fram and Padmananda Rama contributed to this report.