A total of four people including the two men shot by police have now been arrested in connection with the killing - and the latest two arrested were being questioned at a south London police station.
The two men who were shot, aged 22 and 28, have been arrested on suspicion of murder and remain in hospital in a stable condition with non life-threatening injuries.
Scotland Yard said six residential addresses were searched today as part of the investigation - three in south London, one in east London, one in north London and one in Lincolnshire.
'This is a large, complex and fast-moving investigation which continues to develop,' a spokesman said. 'Many lines of inquiry are being followed by detectives and the investigation is progressing well.'
Officers recovered various items from the scene and were appealing for witnesses to send in footage and photographs of the incident. A post mortem was taking place on Drummer Rigby's body today.
Tonight U.S. President Barack Obama issued a statement to say: ‘I condemn in the strongest terms the appalling attack against a British service member in Woolwich on May 22.
‘The United States stands resolute with the United Kingdom, our ally and friend, against violent extremism and terror.
'There can be absolutely no justification for such acts, and our thoughts and prayers are with the family of the victim, the police and security services responding to this horrific act and the communities they serve, and the British people.’
Earlier tributes were paid to Drummer Rigby, 25, from Crumpsall, Manchester who had a two-year-old son. He was from 2nd Battalion The Royal Regiment of Fusiliers, and was attached to the Regimental Recruiting Team in London.
A shocked and tearful neighbour outside the family home in Middleton, Greater Manchester, who did not want to be named, said: ‘He had always wanted to be in the army since he was knee high.’
A steady stream of relatives and friends visited the house throughout the day to support the family. Police and PCSOs also stood guard outside the house and patrolled the street.
A life-long Manchester United fan, he had also stood outside the Royal Palaces as part of his battalion's public duties commitment.
The Rt Rev Mark Davies, The Bishop of Middleton, said: ‘The nation has been shocked by Lee's death. But the greatest burden is carried by those he knew and loved. Our prayers and sympathies are with his family, friends and those he served with.’
Drummer Rigby was brutally murdered in the street in Woolwich, south east London, yesterday by two attackers who were British and of Nigerian descent.
The pair, who were shot by police, were known to security services, and apparently shouted ‘Allah Akhbar’ as they struck. It is believed that the serving soldier was run over and then hacked to death, yards from a primary school.
Alfie Swain, who said he had met Drummer Rigby, told BBC News: ‘I can't explain it, how much it hurts. It's just disappointing.
‘I'd met him in and out of the Army base itself. Hearing that he's gone is just destroying. He was a nice man. He was caring, loving. To hear that he's gone is just disappointing.
Eyewitnesses said that one of the attackers charged towards officers clutching bloodied weapons including a meat cleaver, while the other brandished a gun.
One chilling video clip showed a man with heavily blood-stained hands claiming the killing was committed in the name of Allah and ranting about the Government.
He said: ‘We swear by almighty Allah we will never stop fighting you.’ The attacker went on: ‘We must fight them as they fight us. An eye for an eye, a tooth for a tooth.’
Today officers searched the former home of a man called Michael Adebolajo in Saxilby, Lincolnshire, as well as other addresses in London.
This afternoon two police vans were stationed outside a ground-floor flat in east Greenwich, south-east London, with about a dozen officers positioned outside. The front door of the flat in Eastney Street, had been shattered.
Another neighbour Nicola James, 45, said she believed one of the men arrested over the Woolwich incident was in a relationship with one of the two women who live at the Greenwich flat.
Ms James said she had not seen the other suspect around the housing estate, but added: ‘He was always out in Woolwich, giving out radical leaflets.’
Following a meeting of the Cobra emergency response committee today, Prime Minister David Cameron said the attack had ‘sickened’ the country.
He said: ‘This country will be absolutely resolute in its stand against violent extremism and terror. We will never give in to terror or terrorism in any of its forms.’