President Obama on Thursday downplayed the prospect of any imminent U.S. airstrikes in Syria, saying "we don't have a strategy yet" and stressing that military advisers are still reviewing options for confronting Islamic State militants.

At the same time, the president bluntly ruled out U.S. military action for dealing with another international crisis -- mounting evidence of Russian incursions into eastern Ukraine. "We are not taking military action to solve the Ukrainian problem," Obama said.

The president addressed both crises during remarks in the White House briefing room late Thursday afternoon, as Congress prepares to return from the summer recess. In recent days, lawmakers on both sides of the aisle have demanded that the U.S. strategy for targeting the Islamic State be put to a vote on Capitol Hill, amid speculation the military campaign might expand into Syria.

But Obama stressed Thursday that "we don't have a strategy yet" and pushed back on reports that, he said, suggest the country is about to go "full scale on an elaborate strategy" in the Middle East.

"The suggestion, I guess, has been that we'll start moving forward imminently and somehow Congress, still out of town, is going to be left in the dark," he said. "That's not what's going to happen."

White House Press Secretary Josh Earnest later clarified on CNN that the president referred specifically to Syria when he said there was no strategy yet.

Obama indicated that for the time being, the U.S. will continue to conduct airstrikes in northern Iraq and humanitarian missions, while working politically and diplomatically to "cobble together" a coalition for whatever the long-term strategy is.

To that end, he said he is sending Secretary of State John Kerry to the region to build a "coalition" to confront the threat.

Reports about a potential expanded military campaign follow calls by some lawmakers to strike the Islamic State, also known as ISIS or ISIL, in Syria as well as Iraq. Military leaders have also said the organization will have to be dealt with in some way on the Syrian side of the border.

Obama acknowledged Thursday that he's directed military leaders to prepare a "range of options" on ISIS. He was heading next into a National Security Council meeting where he was expected to discuss the strategy with advisers.

"ISIL poses an immediate threat to the people of Iraq and the people of the region," Obama said, while calling for a "broader, comprehensive strategy."

But he said he doesn't want to "put the cart before the horse."

The president said, once a strategy is formed, there "will be a military aspect to that" and might be a role for an "international coalition" providing air support.

But he was vague on the question of what to do in Syria. Amid speculation over whether the U.S. would ever partner with Bashar Assad to fight ISIS on that side of the border, Obama reiterated his view that "Assad's lost legitimacy."

He said the U.S. would continue to support the "moderate opposition" in the country, giving people a choice other than just Assad or ISIS.

Senate Republican Leader Mitch McConnell, after Obama's remarks, urged the president to develop a "regional strategy" for the Islamic State and present it to Congress and the American people.

"If the President is prepared to engage Congress with a strategic plan to protect the U.S. and our allies from ISIL, I believe he will have significant congressional support," he said. "But don't forget, the threat from ISIL is real and it's growing -- and it is time for President Obama to exercise some leadership in launching a response."

The president's remarks also came amid increased tensions between Russia and Ukraine. Officials in Ukraine say two Russian military columns rolled into the southeastern part of the country after missiles were fired at a border post.

Obama on Thursday blamed Russia for the unrest, saying the country deliberately and repeatedly has violated Ukraine's sovereignty. He said Russia is training, arming and funding pro-Russian separatists in Russia.

Obama, though, said a "military solution to this problem is not going to be forthcoming."

Rather, he said he wants to continue to mobilize the international community to bring pressure on Russia. "This ongoing Russian incursion into Ukraine will only bring more costs and consequences for Russia," Obama said.

Obama said Ukrainian President Petro Poroshenko will visit the White House next month, in what would be his first visit since becoming president. Obama said he also spoke by phone Thursday with German Chancellor Angela Merkel.

In a written statement, though, Sens. John McCain, R-Ariz., and Lindsey Graham, R-S.C., said Russia's actions can only be described as a "cross-border military invasion," adding: "To claim it is anything other than that is to inhabit President Putin's Orwellian universe."

They urged broader "sectoral" sanctions and U.S. and European military support for Ukraine.

"This is a moment to speak and act with clarity. A sovereign nation in the heart of Europe is being invaded by its larger neighbor," they said. "If we will not or cannot defend our own values now, as well as friends who share them, the future will be dark and dangerous indeed, not just for Ukraine but for us too."

At the end of Thursday's remarks, Obama briefly addressed ongoing deliberations over possible executive action on immigration.

Republicans have voiced concern he'll issue a mass reprieve in the coming weeks for illegal immigrants.

Obama did not indicate what he might decide but said: "In the absence of congressional action, I'm going to do what I can to make sure the system works better."

The Associated Press contributed to this report.