Attackers killed Lee Rigby a couple of hundred yards away from the Royal Artillery Barracks in the southeast London district of Woolwich.
"We would like to emphasize that Lee would not want people to use his name as an excuse to carry out attacks against others," the family said in a statement issued Friday by the Ministry of Defence.
The killing has sparked an intense investigation by police. They announced two other arrests in the case Friday, of men seized on suspicion of supplying illegal firearms. Authorities also moved a man arrested on the suspicion of killing Rigby from a hospital to a police station.
Rigby was run over by a car and then stabbed in a daylight attack on May 22.
Since the killing, anti-Muslim actions and angry social media sentiment have emerged in Britain.
But the family stressed that "it would not wish any other families to go through this harrowing experience and appeal to everyone to keep calm and show their respect in a peaceful manner."
Rigby -- who had served as an infantryman in Afghanistan and Cyprus -- "loved life and he loved people," the family statement said.
"He had many friends from different walks of life -- some with different religious beliefs and cultures. But this made no difference to Lee. He always treated others with the greatest of respect," the family said.
The death has been "devastating," and the family is grateful for the public's "overwhelming support," in Britain and all over the world, the statement said.
"We have been amazed by the messages of support we have received from all across the globe. We were deeply touched after visiting Woolwich on Sunday and would like to thank those who were in attendance for giving us the time and space to pay our own tributes to our beloved Lee."
The statement came as Queen Elizabeth II on Friday visited the barracks that housed Rigby -- who worked as a military recruiter as well as a ceremonial drummer. A makeshift memorial of flowers and tributes has swelled on the street outside the barracks in the days since his death.
The monarch met members of the King's Troop Royal Horse Artillery during the visit, which was scheduled before the killing. The troop's duties include firing gun salutes on state occasions and royal anniversaries.
"The queen privately met those who coordinated the barracks response last week to the death of Drummer Lee Rigby," Buckingham Palace said in a written statement.
An inquest into Rigby's death opened Friday at Southwark Coroner's Court and was quickly adjourned.
Detective Chief Inspector Grant Mallon, the senior investigating officer into the death, detailed the circumstances of Rigby's killing:
After working a day at the Tower of London, Rigby was returning to his barracks in Woolwich when a vehicle swerved and struck him. Two men came out of the vehicle and attacked him with cleavers causing him "extensive and serious injuries." The two men moved his "apparently lifeless body" and remained on the scene until police arrived, when "both were incapacitated and detained."
In all, 12 people have been arrested in connection with the killing.
• Michael Adebowale, 22, has been charged with murder and with unlawful possession of a firearm. He was discharged from a hospital Tuesday and has been held in custody since at a police station. He made an initial court appearance Thursday.
• A 28-year-old arrested on the suspicion of Rigby's murder is in custody at a south London police station. The man has been identified by family, friends and acquaintances as Michael Adebolajo. He was discharged from a hospital Friday and transferred to the police station. Police said he was "further arrested" at the station on the suspicion of the attempted murder of a police officer, but didn't provide detail on that charge.
• Two men, ages 42 and 46, have been taken to a south London police station. One was arrested Friday in north London and the other in east London on suspicion of supplying illegal firearms.
• Six others have been freed on bail -- the most recent a 50-year-old man arrested Monday night on suspicion of conspiracy to murder.
• Two were released without charges.
Separately, a man who was arrested after he spoke in an interview about Adebolajo on BBC's "Newsnight" has been charged with two counts of dissemination of terrorist publications and one count of encouragement of terrorism. He is Ibrahim Abdullah-Hassan, also known as Abu Nusaybah. The charges are not connected to the Rigby murder investigation, police said.