The Justice Departments said criminal indictments named Ahmad Umar Agha, 22; Firas Dardar, 27; and Peter Romar, 36, all Syrian nationals.
Arrest warrants were issued for all three on charges including conspiracy, unauthorized access to computers, receiving the proceeds of extortion, money laundering and wire fraud.
The FBI announced that it added Agha and Dardar to its "Cyber Most Wanted" list and offered a reward of $100,000 for information that leads to their arrest. Both are believed to be residing in Syria.
Romar is believed to be living in Germany, according to court documents.
The Syrian Electronic Army (SEA) has been known for hitting news outlets that the group claims slant their reporting of the Syria conflict.
Their most notorious hack was of The Associated Press Twitter account, resulting in a false 2013 tweet saying President Barack Obama had been injured after two blasts at the White House. The message saw the Dow Jones Industrial Average suffer a "flash crash" before traders realized the tweet was false.
Other victims of SEA hacks include the AFP photo department's Twitter account, the BBC, Al Jazeera, the Financial Times and the Guardian.
In 2015, the group took over the accounts of France's Le Monde newspaper, tweeting several messages including one reading "Je ne suis pas Charlie."
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A US investigation said the activity began around 2011 when Agha and Dardar began their campaign in support of the Syrian government and President Bashar al-Assad.
"The conspiracy was dedicated to spear-phishing and compromising the computer systems of the US government, as well as international organizations, media organizations and other private-sector entities that the SEA deemed as having been antagonistic toward the Syrian government," a Justice Department statement said.
Spear-phishing is a technique in which an attacker sends a message disguised to appear as if it were from a trusted source, asking for credentials that enable the hackers to access accounts.
Investigators said the group repeatedly targeted computer systems and employees of the White House but failed to gain access.
Executive Office of the President (EOP). Despite these efforts, at no time was an EOP account or computer system successfully compromised.
At one point, the Syrian group gained control over a recruiting website for the US Marine Corps and posted a defacement encouraging service members to "refuse (their) orders," officials said.
In some cases, the hackers threatened to damage computers, delete data or sell stolen data unless the victims provided extortion payments, prosecutors said. Romar was alleged to be the intermediary to receive extortion payments, which could not be transferred to Syria because of international sanctions.
"While some of the activity sought to harm the economic and national security of the United States in the name of Syria, these detailed allegations reveal that the members also used extortion to try to line their own pockets at the expense of law-abiding people all over the world," said Assistant Attorney General John Carlin.
"The allegations in the complaint demonstrate that the line between ordinary criminal hackers and potential national security threats is increasingly blurry."