John Kerry said samples from hair and blood gathered after the attack “tested positive for signatures of sarin”.
The US blames the Syrian government for the August 21 attack.
President Barack Obama has vowed punitive action but wants Congress to vote on it first.
Syria dismissed the delay and said it was ready for any strike.
UN experts have been in Syria gathering evidence to determine whether chemical weapons attacks have taken place on various occasions. They have now arrived in the Netherlands with samples for analysis.
The biggest and deadliest apparent attack took place on August 21 in east Damascus. The US says more than 1,400 people were killed.
Washington said only the Damascus government has the capacity to launch such an attack.
Syria has denied it was responsible and blames the rebels.
John Kerry implied that the US evidence was supplied by its own sources, rather than via the UN inspectors.
“In the last 24 hours, we have learned through samples that were provided to the United States that have now been tested from first responders in east Damascus and hair samples and blood samples have tested positive for signatures of Sarin,” Kerry said on NBC’s Meet The Press.
“So this case is building and this case will build.”
The US has previously said it had similar evidence of sarin use in other attacks.
John Kerry also said he was confident that Congress would give its approval for the US to launch strikes against Syria after it reconvenes on September 9.
Congressmen “will do what is right because they understand the stakes”, he said, declining to explain whether Barack Obama would press ahead even if Congress voted against.
Syrian Deputy Foreign Minister Faisal Mekdad said Barack Obama’s decision to delay the strikes pending a vote in Congress was just “a political and media manoeuvre”.
Syrian President Bashar al-Assad remained defiant on Sunday, saying: “Syria… is capable of facing up to any external aggression just as it faces up to internal aggression every day, in the form of terrorist groups and those that support them.”
The Syrian government has been fighting rebel forces since March 2011.
More than 100,000 people are estimated to have died in the conflict, and at least 1.7 million have become refugees.
Syria is known to have extensive supplies of chemical weapons.
Barack Obama has often said that using them would cross a “red line”, prompting US intervention.
On Saturday, Barack Obama said any action would be limited, ruling out a ground invasion.
Congress is due to reconvene on September 9, meaning any military operation would not happen until then.
The opposition Syrian National Coalition (SNC) said President Barack Obama’s decision to delay any strikes in Syria was a “failure in leadership” and could “embolden” the forces of President Bashar al-Assad.
Arab League foreign ministers are meeting in Cairo on Sunday, with Saudi Arabia urging them to back calls for strikes against Syria.
The UK has ruled out taking part in any attack, after PM David Cameron failed to win the support of parliament last week.
That leaves France as the only other major power that has said it could strike against Syria – though it says it will not act on its own before the vote in the US Congress.
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