Federal authorities were investigating one of the gunmen involved in Sunday's attack on a Texas cartoon contest featuring images of the Muslim prophet Muhammad, as counterterrorism investigators worked to determine whether the men had any formal ties to the Islamic State terror group.

A federal law enforcement official told the Associated Press that authorities had an open investigation into Elton Simpson at the time of the shooting, in which Simpson and his roommate Nadir Soofi wounded a security guard before being killed by a Garland, Texas police officer. The official was not authorized to discuss the ongoing investigation by name and spoke on condition of anonymity.

It has previously been reported that Simpson was on investigators' radar because of his social media presence. A final tweet from an account linked to Simpson was posted about 20 minutes before the attack and said: "May Allah accept us as mujahideen," or holy warriors. Among the hashtags used by the account was "#texasattack."

Rep. Michael McCaul, R-Texas, the chairman of the House Homeland Security Committee, said Tuesday that authorities had been tracking that Twitter account. He also said that the Department of Homeland Security and the FBI had issued a joint intelligence bulletin to local law enforcement April 20 warning that the Garland event was a possible target for a terrorist attack. The bulletin said that social media accounts linked to extremists had been focusing on the contest. 

McCaul said that the bulletin had resulted in increased security around the event. According to mainstream Islamic tradition, any physical depiction of the Prophet Muhammad — even a respectful one — is considered blasphemous.

The Islamic State group, also known as ISIS, claimed responsibility for the attack in an audio statement Tuesday. The statement on the extremist group's Syria-based Al Bayan radio station called the men "two soldiers of the caliphate."

McCaul said Tuesday that the evidence does not indicate the attack was directed by the Islamic State group, "but rather inspired by them ... This is the textbook case of what we're most concerned about."

However, a counterterrorism source told Fox News Tuesday that data mining in the wake of the Texas attack has revealed a striking connection between at least one of the gunmen and established twitter handled overseas, suggesting that ISIS operatives had knowledge of the attack beforehand, and that the same fighters mentored or encouraged at least one of the shooters.   

Within several hours of the attack, the source said, established ISIS twitter handles had "timely knowledge of the attack," suggesting foreknowledge of the plot. Those handles included a British jihadi in Syria who does not tweet on a regular basis, yet praised both gunmen within an hour of the shooting.

A second established ISIS Twitter handle suggested he had been in contact with one of the shooters prior to the attack, using phrases suggesting that he tried to reach the attacker but just missed him. The source said the social media appeared to show encouragement and mentoring.

The law enforcement official told AP investigators will be studying the contacts Simpson and Soofi had prior to the shooting, both with associates in the U.S. and abroad, to determine any terror-related ties.

The families of Simpson and Soofi say they were shocked by what happened and never saw any signs that either of them was capable of such violence.

Simpson, who was born in Illinois, was arrested in 2010 after being the focus of a four-year terror investigation. But despite amassing more than 1,500 hours of recorded conversations, including Simpson's discussions about fighting nonbelievers for Allah and plans to link up with "brothers" in Somalia, the government prosecuted him on only one minor charge — lying to a federal agent. He was sentenced to three years of probation and ordered to pay $600 in fines and court fees.

It's unclear at what point in his life Simpson turned radical, nor was it immediately clear when or how he met Soofi. 

Soofi did not appear to leave as big an online footprint as Simpson. However, , according to a Facebook account that has now been disabled, the 34-year-old had a longstanding hatred of police and had studied overseas in Pakistan.

Soofi, who was born in the Dallas area, was an undergraduate pre-medicine major at the University of Utah from fall of 1998 to the summer of 2003, said university spokeswoman Maria O'Mara. She said he did not earn a degree.

Utah court records show Soofi had several brushes with police during his time in the state. He pleaded to possession of alcohol by a minor, alcohol-related reckless driving and driving on a suspended license in 2001, court records show, and misdemeanor assault the following year.

Fox News' Catherine Herridge and the Associated Press contributed to this report.