A local TV station reported on Sunday that more than 20 people had been injured in the shooting, citing investigators on the scene.
The state agency declined to answer questions or provide further detail during a news conference on Sunday.
"We're going to continue to work in a very methodical way to go through this scene, to look at the facts and ensure that justice is brought to bear for the families," Jeremy Burkett, a sergeant with the Alabama Law Enforcement Agency, said.
The shooting occurred at 10.34pm on Saturday, according to the agency.
Officials provided no information about what led to the shooting in the town with a population of about 3000 and it was not known if any suspects had been taken into custody.
"What has our nation come to when children cannot attend a birthday party without fear?" President Joe Biden said in a statement on Sunday.
Biden called the rising gun violence in the US "outrageous and unacceptable," and urged Congress to pass laws that would make firearms manufacturers more liable for gun violence, ban assault weapons and high-capacity magazines, and require safe storage of firearms and background checks for gun sales.
Tallapoosa County Schools Superintendent Raymond Porter said at the news conference that counselling would be provided at area schools on Monday and asked local clergy to help families through the situation.
"We will make every effort to comfort those children and don't lose sight of the fact that those are the ones most impacted by this situation," Porter said.
Alabama Governor Kay Ivey said in a Twitter post on Sunday morning that she was staying "closely updated" by law enforcement as details emerged.
"This morning, I grieve with the people of Dadeville and my fellow Alabamians," she wrote in the post.
"Violent crime has NO place in our state."
