Lamb said Wednesday's operation involved US forces and the Iraqi police and army.
He said seven people had been detained. The Iraqi defence ministry said two fighters had been killed and 11 suspects of varying nationalities detained.
Two residents told Reuters they saw a large armoured force of US and Iraqi troops enter Haifa Street in the early morning.
They said the troops clashed with armed men near a cemetery and US snipers were on rooftops.
The Sunni Muslim Scholars Association condemned the raid, calling it "a campaign of genocide" and said a number of buildings had been demolished and people killed.
The US military said Wednesday's mission was "not an operation designed solely to target Sunni insurgents, but rather aimed at rapidly isolating all active insurgents and gaining control of this key central Baghdad location".
Security sources said a helicopter owned by Blackwater, a US security company, that crashed in the area on Tuesday was forced down after the pilot was shot dead.
Three others on board the aircraft, which had been guarding a diplomatic convoy on the ground, may have been shot on landing, they said, although other reports suggested they died when the aircraft crashed.
A fifth person on a second Blackwater helicopter was also shot dead.
Zalmay Khalilzad, the US ambassador to Iraq, paid his condolences to the security contractors, who helped protect US embassy personnel, saying he had known them personally.
"We lost five fine men. It was a very bad day yesterday."