The alleged sender, Paul Kevin Curtis, 45, is a resident of Mississippi.
Initial tests on the letters, identified at remote facilities, showed the presence of ricin, a lethal toxin.
The FBI has said there is “no indication of a connection” between the letters and Monday’s deadly attack in Boston.
The letters addressed to President Barack Obama and Republican Mississippi Senator Roger Wicker were both postmarked Memphis, Tennessee, and dated April 8.
According to US media citing intelligence sources, the letters read: “To see a wrong and not expose it, is to become a silent partner to its continuance.”
The letters were reportedly signed: “I am KC and I approve this message.”
The FBI said Paul Kevin Curtis also allegedly sent a third letter positively identified for ricin to a Mississippi justice official.
The contents of the letter intended for Barack Obama were being sent to an accredited laboratory for further analysis, the FBI said, with results expected in 24 to 48 hours.
Earlier, police questioned a man in the near the Capitol who had a backpack containing sealed envelopes, but he was not taken into custody.
Reports of suspicious packages and envelopes also led to areas within two Senate office buildings being cleared temporarily.
Meanwhile Democratic Senator Carl Levin said an aide had received a suspicious-looking letter and that the authorities were investigating. The staff member had no symptoms, Senator Carl Levin said in a statement, but was staying overnight in hospital as a precaution.
All congressional mail has been sorted and tested off-site since letters laced with anthrax were posted to two senators in 2001.
A spokesman for the Secret Service, which protects the US president and his family, said it was liaising with the Capitol Police and the FBI to trace the origins of the letters.
Ricin, extracted from castor beans, is 1,000 times more toxic than cyanide.
The toxin can be fatal when inhaled, swallowed or injected, although it is possible to recover from exposure.
BKIgkZnVh1MImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…