President Obama said Thursday that the U.S.-led fight against the Islamic State is making progress in spite of high-profile terrorist attacks, while Republican nominee Donald Trump charged that Mr. Obama has allowed the Islamist extremist group to rampage “out of control.”

“We’re going to keep going after ISIL aggressively,” Mr. Obama said at the Pentagon, using an acronym for the group. “We continue to take out senior ISIL leaders and commanders.”

Mr. Obama also hit back at Republican critics, including Mr. Trump, who accused the administration of paying $400 million in ransom to Iran to gain the release of five American hostages in January.

“We do not pay ransom for hostages,” Mr. Obama said. “We didn’t here, and we won’t in the future.”

The president said the Islamic State hasn’t had a major success in Iraq and Syria in a year. But Mr. Obama acknowledged that “lone wolf” attacks are on the rise, saying “the decline of ISIL in Syria and Iraq appears to be causing it to shift to tactics” in other countries.

“It is still very difficult to detect and prevent” such attacks, he said.

Mr. Trump, speaking at a campaign rally in Portland, Maine, blasted Mr. Obama and Democratic nominee Hillary Clinton for allowing the Islamic State to gain strength, committing beheadings and other horrific attacks around the globe.

“We haven’t seen this since medieval times,” Mr. Trump said. “It’s gotten out of control, and Obama has let it get out of control. The Obama-Clinton foreign policy has handed huge portions of Iraq, Libya and Syria to ISIS.”

Mr. Trump also accused the administration of paying ransom to Iran, a sponsor of terrorism.

“I wonder where that money really goes, by the way,” the Republican nominee said. “Either in [Iran‘s] pockets … or toward terrorism. Probably a combination of both.”

Mr. Trump again claimed that a video that he purports shows the money transfer “was given to us — has to be — by the Iranians. And you know why the tape was given to us? They want to embarrass our country.”

Reports surfaced this week that the administration airlifted pallets of foreign currency in an unmarked cargo plane to Tehran just as the Iranians were releasing the American hostages.

The administration said at the time that Iran was receiving a payment for a decades-old arms deal that was never completed, but officials did not disclose back then how the money transfer was taking place.

Justice Department officials objected at the time, believing that it would appear to be a ransom payment and that the Iranians would portray it that way.

The Iranians did claim it was a ransom payment, and now Republican lawmakers are calling on Secretary of State John F. Kerry to explain the deal.

Mr. Obama said the only new detail was the cash involved, and he said it was because the administration’s strict sanctions precluded a normal banking transfer.

“The only bit of news on this is the fact that we paid cash,” Mr. Obama said. “We could not send them a check and we could not wire them the money. The reason cash was exchanged was because we don’t have a banking relationship with Iran.”

He said the payment itself “wasn’t a secret.”

“We were completely open with everyone about it,” Mr. Obama said.

The president slammed his critics for “the manufacture of outrage” over the story, saying they’re looking for more ways to undermine the administration’s nuclear deal with Tehran.

“It’s now been well over a year since the agreement with Iran to stop its nuclear program was signed,” he said. “By all accounts, it has worked exactly the way we said it was going to work.”

The Islamic State has carried out or inspired a series of horrific attacks in the past year, from Orlando, Florida, to Nice, France. Public opinion polls show that more than 60 percent of Americans disapprove of Mr. Obama’s handling of the extremist group.

Mr. Obama met with top military and national security officials at the Pentagon to assess the fight against the Islamic State, including a renewed air campaign against extremist targets in Libya. The meeting included Vice President Joseph R. Biden, Defense Secretary Ashton Carter, CIA Director John Brennan and other Cabinet secretaries and military chiefs.

The meeting came as the U.S. began bombing Islamic State targets this week in and around the Libyan city of Sirte.

The extremist group’s expansion into Libya and elsewhere in North Africa has alarmed European nations that have suffered horrific terrorist attacks this year, such as France and Germany.

The Islamic State began moving into Libya from Syria and Iraq after the ouster of longtime leader Moammar Gadhafi in 2011.

Although U.S. officials say the Islamic State has lost about 40 percent of its territory in Iraq and Syria, the group still holds Iraq’s second-largest city, Mosul. New assessments also show the Islamic State has branched out to as many as 31 other countries, including Libya, Algeria, France, Belgium, Germany and the U.S.

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