The offices of Nuri al-Maliki, Iraq's prime minister, and Jalal Talabani, the president, both issued statements condemning the blast that they said killed 18 people.
Al-Maliki's office said the dead included 12 children, while Talabani's office said all 18 were children.
Sheikh Hamid said the truck, loaded up with logs, was parked next to the pitch and detonated as the boys played.
A defence official confirmed that 18 children were killed and 20 wounded in the latest attack
However, the US military told reporters that it was unaware of the bomb attack and had earlier undertaken a controlled blast in the city.
Major Jeff Pool, a US military spokesman, said the blast by US soldiers near a football field in Ramadi had slightly wounded 30 people, including nine children.
Pool said it was carried out in the courtyard of a building where bags of explosives had been found and that the wounded had cuts and bruises.
Windows from a nearby building were blown out, causing the wounds. Pool said US forces helped evacuate those injured.
He said: "I can't imagine there would be another attack involving children without our people knowing."
The major said the controlled blast in Ramadi was "stronger than we had expected".
The US military often carries out controlled explosions in Iraq to destroy captured weapons or unexploded bombs.
Referring to the football attack, a police colonel in Ramadi, who declined to be identified, said a suicide bomber had detonated a truck bomb and put the time of the explosion at about 5pm.
Pool said the controlled US blast was at 5:34pm.
Ramadi is the capital of Anbar province, the base for Sunni Muslim fighters in Iraq, and is fast becoming a battlefront between rival Sunni factions.
A truck bomb near a Sunni mosque in the city killed 52 people on Saturday, a day after the mosque's imam had made a speech criticising al-Qaeda in Iraq, which is entrenched in the area.
On Monday, a suicide bomber blew up an ambulance at an Iraqi police station near Ramadi, killing 14 people including women and children.
The attacks have signalled increasing conflict between al-Qaeda and Sunni tribal leaders opposed to the group, officials have said.
The incidents underscore the violence gripping Iraq, even as US and Iraqi forces step up a new security plan in Baghdad.
Washington is sending extra troops to Anbar.