Reid, D-Nev., had scheduled a procedural vote Wednesday to begin formal debate on the resolution, but he announced late Monday it was being put off to give President Obama more time to convince Congress and the American public a retaliatory strike is the right thing to do, USA Today reported.
"What we need to do is make sure the president has the opportunity to speak to all 100 senators and all 300 million American people before we do this," Reid said.
The delay came amid a rising number of announcements by senators opposed to military action and followed reports that Syrian officials have floated an offer to turn over the country's cache of chemical weapons to Russia or other nations, something Obama indicated could defuse the need for U.S. military intervention, the newspaper said.
"I have no idea what's going on. It'd be great if the Russians could convince Assad to turn over his chemical weapons to the international community," Sen. Lindsey Graham, R-S.C., said. "That'd be a terrific outcome. I just am very dubious and skeptical."
Obama told NBC Russia's offer to shift Syria's chemical weapons arsenal to international control is a "potentially positive development."
A Senate Democratic leadership aide told the network the potential diplomatic deal was "a major factor" in Reid's decision to put off the vote.
"Members want to see how things develop instead of being locked into a schedule," the aide said.
White House Chief of Staff Denis McDonough had said Sunday the case that Syrian President Bashar Assad's forces had used chemical weapons on his own people had been solidly made.
"Nobody now debates the intelligence, which makes clear -- and we have high confidence about this -- that in August, the Assad regime used chemical weapons against its own people," he maintained on CNN's "State of the Union," part of a blitz of interviews he did Sunday on every major TV network.
"Congress has an opportunity this week to answer a simple question -- should there be consequences for him for having used that material?"
Assad denied in a CBS and Public Broadcasting Service interview airing Monday he had anything to do with the Aug. 21 attack in suburban Damascus, which the Obama administration alleges killed more than 1,400 people, including hundreds of children.
Assad said he didn't even know if an attack with chemical weapons had taken place, although if one did, the rebel opposition may have been behind it, he said, repeating an early allegation the Obama administration and opposition leaders deny.
The Obama administration was trying a full-court press to win the hearts and minds of Capitol Hill lawmakers returning from summer recess and regular U.S. citizens.
Secretary of State John Kerry, Defense Secretary Chuck Hagel and national security adviser Susan Rice were to brief the entire House on U.S. intelligence assessments in a closed-door session at 5 p.m. EDT Monday, officials said.
Obama's scheduled was packed with interviews with ABC, CBS, NBC, PBS, CNN and Fox News Monday afternoon.
The president is to go to Capitol Hill Tuesday to meet with Senate Democrats and follow that meeting with a nationally televised prime-time address Tuesday evening.
In that address, he is expected to argue not punishing Assad for his alleged use of chemical weapons would embolden not just his regime but also Assad allies Hezbollah, Lebanon's Shiite Islamic militant group and political party, and Iran, an administration official told The Washington Post.
Obama joined a Sunday night dinner Vice President Joe Biden held at the vice president's residence for about a dozen Republican senators in the hope of winning over skeptics.
Some lawmakers say they remain unsure who was responsible for the attack or are unconvinced a strike would be the appropriate response.
Lawmakers opposing military action include an unusual alliance of liberal Democrats, who often support Obama, and strident Republican critics.
As part of the administration's "flood the zone" strategy, McDonough will meet with House Democrats and Rice is to meet with the Congressional Black Caucus, whose members are in both chambers.
The resolution, as it stands, backs a military mission designed, in part, to change the momentum of the Syrian civil war and set the stage for Assad's departure.
The House -- where opposition to military action is believed stronger than in the Senate, despite backing by House Speaker John Boehner, R-Ohio, and House Majority Leader Eric Cantor, R-Va. -- isn't expected to vote until the Senate acts.
White House officials, including Obama, have argued if Congress fails to pass a resolution the United States would lose credibility on the international stage.