US intelligence did everything by the book in investigating terrorist Tamerlan Tsarnaev, and couldn’t have reasonably foreseen his attack on the Boston Marathon, President Obama said this morning.

Still, the FBI has launched thorough review of the intelligence community’s handling of Tsarnaev, following tips from Russian authorities in 2011 that the ethnic Chechen immigrant might have radical Islamic beliefs.

“They [federal authorities] not only investigated the older brother, they interviewed him,” Obama said. “They concluded there was no signs he was engaged in extremist activity.”

Obama concluded: “Based on what I’ve seen so far, the FBI performed its duties. Department of Homeland Security did what it’s supposed to be doing.”

Tamerlan Tsarnaev was killed on April 19, four days after set off a bomb at the Boston Marathon, killing three spectators.

The dead bomber’s little brother was arrested hours after Tamerlan’s death and has been charged with allegedly setting off the second explosive.

“When an event like this happens, we want to go back and review every step that was taken,” Obama told reporters today. “We have to leave no stone unturned. We want to see if there was, in fact, additional protocol and procedures that could be put in place.”

Meanwhile, investigators discovered female DNA on the remnants of the bombs used in the Boston Marathon attack, according to a report.

The discovery does not mean a woman helped the bombers, because the DNA could have come from someone involved in selling or manufacturing the bomb components or from something like a stray hair, The Wall Street Journal reported.

But federal agents are taking the discovery seriously and want to know if the DNA can be linked to the wife of one of the terrorists, bomber Tamerlan Tsarnaev.

The FBI has reportedly sought a DNA sample from Katherine Russell, Tsarnaev’s widow — and were last night spotted carrying a bag labeled DNA from the home in Rhode Island where she has been staying with her parents.

Russell and the young daughter she had with Tsarnaev have been holed up at her family’s home since he was killed in a shootout with police four days after the April 15 attack.

Russell has not been charged, and her lawyer said she is doing all she can to aid the investigation.

Tamerlan and his brother, Dzhokhar, are accused of carrying out the attack, which killed three and wounded more than 260.