The documentary "Kony 2012" has been viewed more than 40 million times on the Internet since Monday.
The activist group Invisible Children used social media to promote the film about Kony's brutal tactics in northern Uganda over two decades that resulted in thousands of deaths and the kidnapping of children who were forced to become soldiers in his Lord's Resistance Army, observers said.
U.S. Rep. Ileana Ros-Lehtinen, R-Fla., chairwoman of the House Foreign Affairs Committee, expressed her support this week for efforts to remove the threat of the LRA.
Kony was indicted by the International Criminal Court in 2005 on more than 30 alleged violations of international law, including war crimes, but remains at large.
The Invisible Children film asks viewers for their help in raising awareness about Kony in the hope it might keep pressure on Ugandan and U.S. officials who are trying to find him.
The group specifically asked people to share their comments on social media so "Kony's name is everywhere," The New York Times reported.
Critics say the issue has been too simplified by the film.
Kony fled northern Uganda six years ago and the remaining members of his group, many of whom were kidnapped children, are living in the jungles of neighboring countries.
"What that video says is totally wrong, and it can cause us more problems than help us,"said Dr Beatrice Mpora, who runs a community health organization in Gulu, Uganda, where the rebels were once based.
"There has not been a single soul from the LRA here since 2006," she told Britain's Telegraph. "Now we have peace, people are back in their homes, they are planting their fields, they are starting their businesses. That is what people should help us with."
Invisible Children has also been questioned about its finances, The Telegraph said.
U.S. President Barack Obama announced last year he was sending military advisers to central Africa to help regional troops fight the rebel group.
"For more than two decades, the Lord's Resistance Army has murdered, raped and kidnapped tens of thousands of men, women, and children in central Africa," Obama said in a letter to congressional leaders last fall.
"The LRA continues to commit atrocities across the Central African Republic, the Democratic Republic of the Congo and South Sudan that have a disproportionate impact on regional security."