The four champions were among 10 athletes from five former Soviet countries whose samples revealed banned substances, the International Weightlifting Federation said late Wednesday.
The four Kazakhs included men's 94-kilogram champion Ilya Ilyin, and women's gold medalists Zulfiya Chinshanlo (53kg), Maiya Maneza (63kg) and Svetlana Podobedova (75kg).
If all four are disqualified, Kazakhstan would drop from 12th to 23rd in the 2012 medal standings.
Earlier, Kazakhstan's Olympic committee said its athletes recorded five positives in retests from Beijing and London.
Three more medalists tested positive: Russia's Apti Aukhadov, who won silver at 85kgs, Ukraine's Yuliya Kalina, bronze at 58kgs, and Belarus' Marina Shkermankova, bronze at 69kgs.
Completing the group of doping positives were Boyanka Kostova from Azerbaijan, and Dzina Sazanavets and Yauheni Zharnasek of Belarus.
The IWF said that more information about the IOC retesting of samples taken at the 2008 Beijing Games, where 10 cases were "presumed" positives that required B sample analyses, would be released "as soon as possible."
The 20 cases among weightlifters account were among 55 total positives which the IOC has reported so far, including 32 from Beijing and 23 from London.
The IOC is retesting samples to catch cheats who might be competing at the Rio de Janeiro Olympics in August.