Secretary of State John Kerry on Wednesday rebuffed Russia's demand that U.S. warplanes leave Syrian airspace to make way for their own airstrikes, saying coalition forces are not going anywhere. 

"These strikes will continue," Kerry said. 

Kerry spoke at a United Nations Security Council meeting chaired by his Russian counterpart, Sergey Lavrov, with whom he reportedly spoke before the meeting. The meeting followed a dramatic escalation in the Syrian conflict, as Russia began bombarding opposition targets inside the country. 

Speaking in New York, Kerry said he was prepared to welcome Russia's actions if they are directed only at the Islamic State and Al Qaeda. 

"We would have grave concerns should Russia strike areas where ISIL and Al Qaeda-affiliated targets ... are not operating," Kerry said, adding that nations must not confuse fighting ISIS for supporting Bashar Assad. 

Russia says it is striking ISIS positions, but U.S. officials and others cast doubt on that claim. A U.S. defense official noted Russian warplanes have struck targets in Homs and Hama, where there is no ISIS presence.   

Kerry called Wednesday for holding "de-confliction talks" with Russia as early as possible. But he made clear that amid the discussions over Russia's role, U.S. and coalition action would continue. 

According to sources, as Russia launched its airstrikes, Moscow requested the U.S. stay out of Syrian airspace during the missions. But Kerry noted during the U.N. meeting that the coalition conducted strikes within the last 24 hours, including one an hour before his remarks. 

"The United States and the coalition will continue our ongoing air operations as we have from the very beginning," he said. 

Kerry went on to say that the coalition is poised to "dramatically accelerate" its efforts, with additional strikes against ISIS in northwest Syria and increased support for anti-ISIS fighters in northeast Syria. But he said ISIS "cannot be defeated as long as Bashar al-Assad remains president of Syria." 

White House Press Secretary Josh Earnest also said the Defense Department is "reviewing" Russia's actions. He said the U.S. welcomes "constructive" Russian contributions, but raised concern that Russia is ramping up support for Assad. 

Meanwhile, Russia's aerial bombardment against Syrian opposition targets raised bipartisan alarm on Capitol Hill Wednesday -- with some echoing concerns that Russia's airstrikes will not distinguish between Islamic State targets and moderate opposition forces. 

"These airstrikes are indiscriminate in nature," Sen. John McCain, R-Ariz., said.  

McCain delivered a blistering floor speech on the developments in Syria, blasting what he called the Obama administration's "leading from behind" approach. 

He said the war has "now created a platform for a Russian autocrat to join with an Iranian theocrat to prop up a Syrian dictator." 

The airstrikes follow a weeks-long military build-up by Russia inside Syria, which led to a flurry of phone calls and meetings between U.S. and Russian officials. That culminated on Monday with a meeting on the sidelines of the United Nations General Assembly between President Obama and Russian President Vladimir Putin.   

But according to one senior U.S. official, Russia has now "bypassed" a process that Obama and Putin agreed on to "deconflict" military operations. 

"That's not how responsible nations do business," the official said. 

A senior U.S. defense official said a Russian official in Baghdad informed U.S. Embassy personnel Wednesday morning that their military aircraft would fly "anti-ISIL missions" over Syria. 

"He further requested that U.S. aircraft avoid Syrian airspace during these missions," the official said -- a request that apparently was rejected. 

"While we would welcome a constructive role by Russia in this effort, today's demarche hardly seems indicative of that sort or role and will in no way alter our operations," the U.S. defense official said. 

McCain said U.S. policies have led to this point. 

"It did not have to be this way," he said. "This is the inevitable consequence of hollow words, red lines crossed ... and a total lack of American leadership. ... This is a very, very, very sad day for America and the world." 

Rep. Adam Schiff, D-Calif., top Democrat on the House intelligence committee, also raised concerns about Russia's military action. 

"The use of Russian military force in Syria adds a troubling new development to a war effort already plagued with problems," he said in a statement. "... The Russian air campaign may be even more destructive if it targets moderate rebel forces fighting the Assad regime. Already, the growing Russian presence has thrown a life line to embattled dictator Bashar al-Assad, at a time when pressure on the regime and its supporters may have finally led to a negotiated end to the conflict." 

He said "the increased longevity of the regime -- made possible by this Russian intervention -- will only prolong the civil war." 

Fox News' Jennifer Griffin and Lucas Tomlinson and The Associated Press contributed to this report.