The chartered flight in Friday's crash arrived from Naval Station Guantanamo Bay, according to Naval Air Station Jacksonville, in a post on its Facebook page.
The cockpit voice recorder is in the tail of the plane and submerged underwater.
The sheriff's office said its marine unit assisted Naval Air Station Jacksonville in the response effort.
All passengers and crew members are "alive and accounted for", the mayor of Jacksonville Lenny Curry wrote on Twitter.
Landsberg said investigators will look closely at whether the weather played a role in the incident.
Note that the Boeing 737-800 is different from the Boeing 737 MAX 8 which was banned from flying after two fatal crashes. When they returned later, they didn't see any pet carriers above water, Connor said.
The commanding officer of NAS Jacksonville, Capt. Michael Connor, called it "a miracle". "Everybody was helping everybody", she said.
He said crews began working to contain any jet fuel leaks nearly immediately after securing the passengers' safety.
The plane was attempting to land at a military base on Friday night when it skidded off the runway, 21 people were injured and they were transported to a nearby hospital for treatment, said authorities.
Several pets were on the plane as well, and their status wasn't immediately clear.
The NTSB tweeted that it is sending a "Go Team", which will investigate with the help of the Naval Air Station.
The Jacksonville Sheriff's office confirmed that there were no casualties and all 136 passengers and seven crew members were safely removed from the aircraft.
Despite crashing into the shallow St Johns River, the 18-year-old plane actually only sustained a small amount of damage.
Associated Press journalists took a boat on Saturday to the spot and reported the chemical stench of oil and fuel is pungent. At least 50 firefighters were involved in the rescue, said Chief Mark Russo of First Coast Navy Fire and Emergency Services.
The National Transportation Safety Board has also launched an investigation into the incident.
The plane arrived four hours late in Guantanamo Bay, and those getting off warned them that the air-conditioning was broken, she said.