President Obama says he told Russian President Vladimir Putin the only way to solve the problem in Syria is a political transition that keeps the state and military intact, but is inclusive with President Assad transitioning out of power. (Reuters)

In his first remarks on Syria since Russian airstrikes began, President Obama said the United States would continue its fight against Islamic State fighters and other extremists, but said "we're not going to make Syria into a proxy war between the United States and Russia."

The president advocated international negotiations to forge a coalition government from Syria's warring factions, but he warned that Syrian leader Bashar al-Assad must leave office at the end of any transition talks.

"The problem here is Assad and the brutality he has inflicted on the Syrian people, and it has to stop," Obama said during a White House press conference Friday. "We are not going to cooperate with a Russian campaign to simply try to destroy anybody who is disgusted and fed up with Mr. Assad’s behavior."

He said Russian President Vladimir Putin had to step up military activities in Syria not out of strength but out of weakness and because Assad's government was failing.

"A military solution alone, an attempt by Russia and Iran to prop up Assad and try to pacify the population, is just going to get them stuck in a quagmire, and it won’t work and they will be there for a while if they don’t take a different course," Obama said.

Obama defended his decision not to get more involved in the Syrian conflict, including by sending more weapons and American troops.

The president said, “I have to make a judgment based on once we start something we have to finish it and do it well, and do we in fact have the resources and the capacity to make a serious impact, understanding that we still have to go after ISIL in Iraq and an Iraqi military weaker than any of us had perceived.”

Amid the wave of refugees fleeing the region, Obama said: “I am under no illusions about what an incredible humanitarian catastrophe this has been.” He called the images of children who have drowned seeking safe havens “heartbreaking.”

He dismissed some proposals for other, more aggressive strategies in Syria as “half-baked ideas” and said that when those who advance them are pressed for military and funding details, “typically what you get is a lot of mumbo jumbo.”

Obama's comment set him up for a question about presidential hopeful and former Secretary of State Hillary Clinton, who on Thursday said that the United States should create "no-fly zones" and "humanitarian corridors" to protect civilians and moderate anti-Assad rebels. Obama said Clinton "is not half-baked in terms of her approach to these problems." But he said that "there's a difference between running for president and being president. And the decisions that are being made and the discussions that I'm having with the Joint Chiefs become much more specific and require, I think, a different kind of judgment." He said "if and when she's president, then she'll make those judgments," adding that "these are tough calls."

While sharply criticizing Putin, Obama also said: "I want Russia to be successful. This is not a contest between the United States and Russia. It is in our interests for Russia to be a responsible actor on the world stage that can share burdens with us … because the problems we have are big."

On federal budget issues, the president said Congress must pass a budget to avoid a "manufactured crisis" that could derail the economic recovery. And he vowed that he would not sign another "short-sighted" continuing resolution to keep government open if Congress cannot agree on a new tax and spending program.

Citing political campaign talk about "the need to be number one," Obama said that passing a budget was a key component of that. “Part of what makes us a leader is when we govern effectively,” he said. “That’s U.S. leadership. When we fail to do that we diminish U.S. leadership. We can’t just keep kicking [this problem] on down the road.”

Obama said that when it comes to the debt ceiling, “historically we do not mess with it. If it gets messed with, it would have profound implications for the global economy.”

He said the administration would not barter other legislative items for an increase in the debt ceiling. “We’re not going to negotiate on that,” he said. “It has to get done in the next five weeks.”

He also warned Congress not to mix the politics of Planned Parenthood with the federal budget.

“You can’t have an issue like that potentially wreck the U.S. economy any more than I should hold the economy hostage so that we do something about gun violence,” he said.

Obama also addressed the latest episode of gun violence at an educational facility.

Obama said he had asked his advisers whether there were executive actions that could help diminish gun violence, “actions we can take that might prevent even a handful of these tragic deaths.”

But he added, “This will not change until the politics change and the behavior of our elected officials change.” And he said that “so what I’m going to do is talk about this.” He urged supporters of gun control to be as organized and effective as the National Rifle Association, which he said “is good at what they do. You have to give them credit.”

He said there was no evidence that American young men were any more violent than young men in other countries. “Our homicide rates are just a lot higher than other places,” he said. “You can’t kill as many people if you don’t have easy access to these kinds of weapons.”

He added: “This is happening every single day in forgotten neighborhoods throughout the country. Kids are just running for their lives just trying to get to school.”

Asked about the visit of Pope Francis, Obama said that "he is a good man with a warm heart and a big moral imagination." He also said the pope had "a good sense of humor. While I can't share all his jokes, they were all clean."

The president spoke after the formal announcement that Education Secretary Arne Duncan would step down at the end of the year and be succeeded by John B. King, Jr., who has been acting as deputy secretary. A former charter school leader in Boston and New York, King joined the Education Department in January after a turbulent tenure as commissioner of education for the state of New York. Duncan, 50, used the federal government's role in 100,000 public schools to bring about landmark changes in areas such as teacher evaluations and higher academic standards.

Obama hailed Duncan as “one of longest-serving secretaries of education in our history and one of the most consequential.” He credited him with prodding 30 states to up their investments in early childhood education and raising standards for teaching. Obama noted that the U.S. high school graduation rate is at an all-time high, and said that Duncan had done much to “bring our education system, sometimes kicking and screaming, into the 21st century.”

Duncan thanked Obama for creating a climate for making good decisions, saying that "on every hard decision his only question was what is the right thing to do for our kids."