Stubb speaking to reporters at a news conference in Moscow on Wednesday.
A former British military officer, who was an OSCE representative in Georgia when the war broke out, told the BBC on Sunday that he had warned of Georgian military activity before the August war but that the reports were not passed on by bosses.
Finnish Foreign Minister Alexander Stubb, who chairs the OSCE, said the organization had only three observers in South Ossetia when the war erupted in August.
"It's not my job to make the judgment on who started the war, or how it actually started," Stubb told a Moscow briefing. "The OSCE isn't an intelligence service. Our instruments are, unfortunately, very limited."
Stubb added that the OSCE did "the best we could" together with the European Union to quickly broker a truce.
Stubb said the OSCE will assist a Swiss-led inquiry into the circumstances that led to the war.
The five-day war erupted when Georgia launched an attack to regain control over South Ossetia, which broke from Georgian control in the early 1990s. Russian forces swiftly repelled the attack and drove deep into Georgia.
After a meeting with Stubb on Tuesday, Foreign Minister Sergei Lavrov said Russia wants to know what OSCE observers reported from the field in Georgia before the war erupted.
Russia and Georgia blame each other for the five-day war, which badly damaged Russian-Western ties.
"We are very interested in knowing the truth about what OSCE observers saw, what they reported and who they reported to," Lavrov told a news conference.