The decision marked a stark turnabout for the White House, which had appeared on the verge of ordering U.S. forces to launch a missile attack against Syria.
Syria's state-run news agency SANA quoted Assad saying that his government is capable of confronting a U.S. strike, but did not carry his exact comments. Assad said earlier this week that Syria "will defend itself" against Western military strikes.
Syria's deputy foreign minister, Faysal Mikdad, claimed Sunday that Obama stepped back from his threat because his administration lacks evidence of Syrian government involvement in purported poison gas attacks.
"The hesitation and the disappointment is so obvious in the words of President Obama yesterday," Mikdad told reporters in Damascus. "The confusion was clear as well."
The Assad regime alleges the Aug. 21 attacks were carried out by rebel fighters, but has not presented proof.
The state-run Syrian daily Al-Thawra, striking a gloating tone, said Obama's decision signaled defeat.
"Whether the Congress gives the red or green light for an aggression, and whether the prospects of war have been enhanced or faded, President Obama has announced yesterday, by prevaricating or hinting, the start of the historic American retreat," wrote the daily, which expresses the Syrian government's thinking.
Kerry said in appearances on several television news shows Sunday that Obama has the right to take action against Syria, with or without Congress' approval.
But he stopped short of saying Obama was committed to such a course even if lawmakers refuse to authorize force. Congress is to return from a summer break Sept. 9.
Kerry maintained there is no weakness in Obama's about-face. "This case (for an attack) is going to build stronger and stronger," Kerry told NBC's "Meet the Press."
He said that "the people of America should be celebrating that the president is not acting unilaterally."
Kerry told CNN's "State of the Union" that hair and blood samples from victims in eastern Damascus have "tested positive for signatures of sarin."
Kerry said the samples were provided to the U.S., and did not come from U.N. chemical weapons experts.
The experts spent a week in Syria, collecting biological and soil samples from stricken areas. U.N. chief Ban Ki-moon said he would present the findings as quickly as possible.
The pope, meanwhile, abandoned the traditional religious theme of the weekly papal appearance to crowds in St. Peter's Square on Sunday and instead spoke entirely, and with anguish, about Syria.