The website that American men use to register for the military draft crashed on Friday (local time) due to "the spread of misinformation", the agency tweeted.
The Selective Service site crashed soon after the announcement that one of Iran's highest-ranking military officers had been killed in a US airstrike at Baghdad International Airport.
Iraqi officials said Major General Qassem Soleimani, head of Iran's elite Quds Force, was killed in the attack, which was ordered by President Donald Trump.
The incident prompted concerns online of the possibility of a new war in the Middle East, and the hashtag "World War III" began trending on Twitter.
"Due to the spread of misinformation, our website is experiencing high traffic volumes at this time," the Selective Service said in a tweet.
"If you are attempting to register or verify registration, please check back later today as we are working to resolve this issue. We appreciate your patience."
The agency added it is "conducting business as usual" after the airstrike.
"In the event that a national emergency necessitates a draft, Congress and the President would need to pass official legislation to authorize a draft."
Tensions between the US and Iran - already strained - spiked in late December after an American contractor was killed in Iraq. US officials blamed Iranian-backed militia Kata'ib Hezbollah for the attack and subsequently carried out military strikes against the militia, killing at least 25 fighters.
That retaliation by the US triggered protests in the streets of Iraq and an attack on the US embassy in Baghdad, which the US blamed on Iranian-backed militia.
The killing of Soleimani was then carried out as a response to that embassy attack.
Currently, all US men aged 18 to 25 are required by law to register with the Selective Service. Not registering is illegal.
Registering is also a requirement to receive federal student aid, which is given to university students from the US Education Department.
The official Federal Student Aid Twitter account said there is no priority order for the Selective Service based on application forms for federal student aid, instead a random lottery number and year of birth are used.
Women don't need to register with the Selective Service, after a federal judge ruled that to be "unconstitutional" in February 2019.
That decision was controversial, however, with District Court Judge Gray Miller, from Houston, saying the argument for excluding women "smacks of archaic and overbroad generalisations about women's preferences", CNN reported.
"While historical restrictions on women in the military may have justified past discrimination, men and women are now similarly situated for purposes of a draft or registration for a draft."
Miller's ruling didn't have an immediate effect because it didn't block the government's current policy.
The Selective Service asked Miller to reject his case because the National Commission on Military, National and Public Service is currently looking at the male-only registration policy.