Story highlights President Barack Obama interviewed by CNN's Wolf Blitzer

Obama said Russian proposal on Syria chemical weapons was a "potentially positive development"

Obama said the the United States would maintain pressure on Syria

The president plans to address the nation on Syria on Tuesday

Russia's proposal for Syria to surrender its chemical weapons to international control was a "potentially positive development," but could be a stall tactic, President Barack Obama told CNN on Monday.

"We're going to run this to ground," Obama said in an interview with CNN's Wolf Blitzer, adding that the United States will work with Syrian ally Russia and the international community "to see if we can arrive at something that is enforceable and serious."

A 'breakthrough' on the horizon?

Obama said the new proposal that emerged Monday from Russia resulted from his threat to attack Syria for violating an international ban on using chemical weapons, as his administration contends occurred on August 21 in suburban Damascus.

He and Russian President Vladimir Putin spoke about the Syrian chemical weapons and the U.S. push for a military response at last week's G20 summit in St. Petersburg, Obama told Blitzer.

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"We have not seen these kinds of gestures up until now," the president said. "The fact that the U.S. administration and I have said we are serious about this, I think, has prompted some interesting conversations."

The Russian proposal could lead to a "breakthrough," but would require follow-up while maintaining pressure on Syria and Russia by continuing his push for Congress to authorize a military attack, Obama said.

In an apparent response to some lawmakers who have questioned U.S. interests in a potential military strike, Obama said Syria's chemical weapons "pose a significant threat to all nations and to the United States, in particular."

"That's why 98 percent of humanity have said we don't use these. That protects our troops, and it protects children like the ones that we saw in those videos inside of Syria," the president said, referring to video footage that showed people writhing near death.

The U.S. government says more than 1,400 people died in the attack.

Obama to keep beating the drum on Syria

Obama will make a televised address from the White House on Tuesday night as part of the administration's offensive to build support for military action in Syria. His interview with CNN was one of six television interviews on Monday in his effort to reach the public directly.

"If we can accomplish this limited goal without taking military action, that would be my preference," Obama said. "On the other hand, if we don't maintain and move forward without a credible threat of military pressure, I don't think we'll actually get the kind of agreement I'd like to see."

Obama told ABC that there was no time limit for an agreement.

Syria welcomed Russia's proposal Monday, paving the way for a possible diplomatic solution to the crisis that comes amid Syria's two-year civil war that has killed more than 100,000 people, according to U.N. estimates.

Obama acknowledged that an agreement on the Russian proposal may not solve Syria's underlying civil war, "but it does solve the problem that I'm trying to focus on right now, which is making sure that you don't have over 400 children gassed indiscriminately by these chemical weapons."

When asked by PBS about Syrian President Bashar al-Assad's claim that the U.S. is lying about his use of chemical weapons, Obama said there can be no diplomatic solution if the Syrian president keeps make statements that are "untrue."

"I think that if we can come up with a mechanism to get these under control, verify and enforce that they are not being used, then we should do everything we can to pursue that," Obama said. "But ... that's not going to happen if Assad thinks that he can lie his way through this and eventually the world forgets the images of those children who were gassed."

Al-Assad's military lacks capability, Obama said

Obama also sought to tamp down the specter of a threat from Assad for the United States to "expect every action" in retaliation for potential military strikes in Syria.

"Mr. Assad doesn't have a lot of capability. He has capability relative to children, he has capability relative to an opposition that is still getting itself organized and are not professional trained fighters," Obama said. "He doesn't have a credible means to threaten the United States."

However, Obama said it was possible for Iran and Hezbollah to launch "asymmetrical strikes," but dismissed them as nothing more than "the kinds of threats that we are dealing with around the world."

He told NBC that he had yet to decide how he would proceed if Congress voted against authorizing force.

In light of the upcoming anniversary of the 9/11 terror attacks, Obama said the date brings heightened security, but he cautioned that "we're not going to be able to protect ourselves 100 percent of the time against every threat" and that the key was to be prepared without over-reacting.