Max, which has headquarters in London, said its UTS-15 appraisal well encountered excellent quality reserves during drilling in the Uytas field.
"Reservoir quality is excellent," the company said in a statement Wednesday.
The Kazakhstan-focused energy company said it was planning at least six more wells as part of an initial appraisal program in Uytas.
Max in April said it estimated the reserve potential at the Uytas field in Kazakhstan at 778 million barrels of oil.
Kazakhstan hosts the Kashagan oil field, one of the largest in the world, with as much as 16 billion barrels of estimated commercial reserves.
The company said Wednesday it has started drilling its first appraisal well on the Eskene North field. Max offered no reserve expectations for Eskene North.
The U.S. Energy Information Administration, the statistical arm of the Energy Department, estimates Kazakhstan holds as much as 30 billion barrels of oil reserves.