London's mayor dismissed fears a permanent monument might become a magnet for extremists.
Lyn Rigby speaks exclusively to Good Morning Britain about her ongoing grief and described why she will never forgive her son's murderers.
In her only television interview since the verdict, she told ITV News that she begs forgiveness from Lee Rigby's family.
Today, the Department for Communities and Local Government said: "Britain has a long tradition of memorials to pay respect to the fallen through public subscription, including memorials to mark acts of IRA terrorism on the British mainland."
The DCLA added: "Provided such a memorial has the support of Drummer Lee Rigby's family, the Government is happy to endorse a proposal for an appropriate memorial, such as a memorial plaque, in Woolwich."
Organiser Julia Stevenson read a poem sent by Lee Rigby's mother, Lyn Rigby:
The day is fading and the night is drawing near, the setting of the sun for a life we hold so dear.
The darkness is not forever, for again the day will come, and new light will surround us and engulf us all as one.
We'll manage through these bad times, we'll struggle through the storm. We'll tread amongst the roses, we'll pull the painful thorn. Yes, we know that we will miss you, but that's for us to bear,
For we know that you are safe now, and you don't have to care. Goodnight our son, brother, uncle, father and soulmate.
Goodnight my fellow soldier friend, goodnight our peaceful warrior. In your memory we'll defend.
Bikers from across the UK are leading tributes to soldier Lee Rigby today. The riders, including current and former British military personnel, are gathering in Greenwich before travelling to Woolwich Barracks, where Fusilier Rigby was stationed, for a memorial service.
Organiser Julia Stevenson, said: "The Lee Rigby ride is about a single soldier brutally cut down not on the battlefield but on the streets of London. In the act of riding through Woolwich on the anniversary of his death we are expressing the admiration and respect we all share for our armed forces."
Julia Stevenson, added: "As we ride we will remember Lee, and our thoughts will be for his family at this difficult time, and his regiment. We will proudly represent a nation who was moved by this tragedy by riding as one."
Speaking to ITV News about calls for a memorial to Lee Rigby, Boris Johnson said: "It would certainly have my support, after all we've got a memorial to WPC Yvonne Fletcher".
The mayor says he's not concerned about a memorial attracting extremists, adding: "The lesson for London is his killers did not succeed in their intent which was to divide the city."
Anniversary of Lee Rigby's murder being marked by a growing row over calls for a memorial in Woolwich. @itvlondon
The Home Secretary Theresa May led tributes to murdered soldiers Lee Rigby, a year since his brutal death.
The 25-year-old was killed near Woolwich barracks in south east London on May 22. Home Secretary Theresa May said:
We shall never forget the appalling crime which was committed so publicly in Woolwich a year ago and our thoughts must go to Lee Rigby's loved ones on this very difficult day.
The entire country united to condemn his death and the murderous ideology his killers espoused. They were swiftly brought to justice and we are committed to doing everything we can to challenge those whose beliefs and behaviour threaten our way of life.