WASHINGTON — Amid growing pressure to act, President Obama on Tuesday cautioned that defeating the Islamic State would take time, even as some Pentagon officials expressed frustration with what they decried as White House foot-dragging on striking the militant group’s Syria sanctuaries.

With U.S. aircraft pressing attacks on Islamic State fighters in Iraq, the administration confronted mounting questions about how it would deal with the al-Qaida spinoff’s presence on Syria’s side of the border. That is a far more complex goal because any setback dealt the group in Syria could benefit Syrian President Bashar Assad, whose ouster is official U.S. policy.

Senior Pentagon officials have been conferring with the White House on hitting Islamic State targets just inside eastern Syria, from where the group launched an atrocity-filled offensive in mid-June that overran roughly half of Iraq and brought it to the outskirts of Baghdad, said two U.S. Defense officials.

The White House, however, has yet to request a formal proposal, said the Defense officials, who expressed frustration over what both separately called the administration’s “dithering.” They spoke on condition of anonymity because they weren’t authorized to discuss the issue publicly.

“The targets would be similar to the ones we struck in Iraq,” said one of the officials, referring to the Islamic State combat vehicles, artillery positions and checkpoints that the U.S. has hit in nearly 100 airstrikes in northern Iraq since Aug. 8.

The officials compared the current situation to Obama’s hesitancy nearly one year ago to make good on a threat to attack Assad’s chemical weapons arsenal after what the United States and its allies charged were regime nerve gas attacks that killed hundreds of civilians.

The administration contends that by withholding those strikes, the United States and Russia were able to broker a deal under which Assad surrendered nearly all of his chemical weapons stocks. But critics portrayed Obama’s decision as a retreat that made the United States look weak, boosted Assad’s international standing, hurt the moderate Syrian rebel movement and spurred new recruits and funding for the Islamic State and other Islamist groups fighting the Syrian leader.

Obama has come under mounting pressure to act against the Islamic State inside Syria since the group posted a video a week ago showing the beheading of American freelance journalist James Foley. The subsequent bellicose reactions by senior administration officials and assertions that the Islamic State can’t be defeated unless it’s hit in Syria boosted expectations that U.S. airstrikes were imminent.

The administration sought to tamp down expectations on Monday even as unidentified U.S. officials told several news organizations that Obama over the weekend for the first time authorized surveillance overflights of Islamic State targets inside Syria.

Even so, the administration faced new demands to disclose a plan to defeat the Islamic State.

Obama owes Americans “a clear and comprehensive plan to reverse the spread of terrorism,” said a statement issued Tuesday by the office of House Speaker John Boehner, R-Ohio.

Speaking on Tuesday to one of the country’s largest veterans’ organizations, Obama appeared to address his critics in asserting that it will take more than military strikes to defeat the Islamic State.

The United States is pressing an incoming Shiite Muslim-led Iraqi government to reconcile with minority Sunnis and Kurds, helping to strengthen the Iraqi army and Kurdish militias, and urging regional powers and U.S. allies to lend their support, he told the annual American Legion conference in Charlotte, N.C.

Obama pledged anew to bring Foley’s killers to justice and defend Americans and the U.S. homeland, saying, “Our message to anyone who harms our people is simple: America does not forget. Our reach is long. We are patient. Justice will be done.”

The president, however, didn’t directly address how he planned to deal with the Islamic State inside Syria.

“We’ll continue to take direct action where needed to protect our people and to defend our homeland. And rooting out a cancer like ISIL won’t be easy and it won’t be quick,” he said, using one of the group’s acronyms.

The State Department and Pentagon declined to discuss the administration’s plans to deal with the Islamic State in Syria, where the group in recent weeks has dealt Assad a series of major setbacks. Bolstered by U.S.-made combat vehicles and artillery captured from the Iraqi army, it has seized more territory in the north and east while capturing key Syrian military bases.

Dealing with the Islamic State inside Syria, where it has set up local administrations, social services and Islamic courts in the roughly one-third of the country that it controls, carries more risks than hitting the group in Iraq, whose government sought U.S. help.

The Islamic State is the strongest of a slew of rebel groups fighting the Assad regime, which is backed by Iran, Russia and Hezbollah, the Lebanese Shiite militia movement. The Islamic State also is at war with the other insurgent groups, including the Nusra Front, al-Qaida’s official Syrian affiliate.

Obama must carefully calibrate any U.S. strikes to ensure that they don’t give undue advantage to Assad. Moreover, any attacks that benefit the other rebel groups also help al-Qaida.

Moreover, Obama would have to stretch his justification for authorizing the U.S. airstrikes in Iraq – where he says they are protecting U.S. diplomatic and military personnel – to any operations in Syria.

Rear Adm. John Kirby, the Pentagon spokesman, refused to confirm that U.S. surveillance flights over Syria have begun.

But he did note that the United States is “not going to hold ourselves to geographic boundaries” to defend Americans.