President Obama said he would put military strikes against Syria on hold if Bashar Assad's government turned over control of its chemical weapons to international observers, but cautioned he would wait to see if Damascus followed through on the Russian proposal.

"Absolutely. If in fact that happens," Obama told ABC News, in one of six interviews he gave Monday, as he seeks to rally support for a strike on Syria.

Just minutes after the interviews aired Senate Majority Leader Harry Reid, D-Nev., said he was postponing a vote on a resolution authorizing action against Syria set for Wednesday.

In a separate interview with CNN’s Wolf Blitzer, Obama said the Russian offer could be a real breakthrough.

“It's possible if it's real,” Obama said. “I think it's certainly a positive development when the Russians and the Syrians make gestures toward dealing with these chemical weapons.”

A cautious Obama though insisted he would have his national security team, including Secretary of State John Kerry, “run this to the ground” to make sure the proposal is “enforceable and serious.”

He also stressed that Russia would not have arrived at this point without the U.S. threat of military strikes.

Kerry offered Assad a last chance earlier Monday morning by saying he could prevent a military strike by handing over his chemical weapons to international inspectors. Kerry, though, expressed skepticism that Assad would accept.

Russia’s foreign minister, however, seized on the idea and said his nation would press Syria to turn over its chemical arsenal to international control.

Assad's government Monday said it welcomed the Russian proposal – the first indication that a diplomatic solution could resolve the international standoff.

The U.S. charged Syria with using chemical weapons in an attack in an eastern suburb of Damascus that killed 1,400 people, including hundreds of children, last month. Assad’s regime and opposition forces have waged a brutal civil war, with thousands of civilian casualties.

Obama is seeking congressional authorization to strike Syria and has declined to rule out acting without the backing of lawmakers. But he faces a tough challenge rallying support in both the House and Senate, with polls showing a strong majority of Americans oppose intervention.

Obama stopped by a Monday afternoon meeting between National Security Adviser Susan Rice and members of the Congressional Black Caucus over Syria in the White House's Roosevelt Room.