Akmatbaev, who is under investigation in a murder case and has been accused of connections to organized crime, is running to fill a seat that has been vacant since his brother, Tynychbek, was killed during a prison siege in October.
The election commission says Akmatbaev received some 79 percent of the vote, although officials stressed that those figures still were not final.
"There will not be a [second-round] runoff in the Balykchy constituency," Commission Chairman Tuigunaly Abdyraimov said today. "Akmatbaev Rysbek Abdimalikovich has won in the first round. All of these [vote counts] are just preliminary results."
Rysbek Akmatbaev in late March
Official questions remain over Akmatbaev's registration as a candidate.
Akmatbaev was acquitted of murder charges in January. But the family of the slain man is appealing, meaning Akmatbaev is still officially under investigation. Under Kyrgyz law, he cannot legally occupy a seat in parliament until the case against him is closed.
There were by-elections to fill two other vacant seats in parliament as well on April 9, but fewer than 50 percent of eligible voters cast ballots. A second round of voting will be held in those constituencies.
(with additional ITAR-TASS reporting)