"Let's not rush. Let us proceed step by step to put the kibosh on anything", said Kononenko during the Live broadcast.
The capsule leak caused a flap between the US and Russian space agencies, following its discovery at the end of August.
It was late August when a mysterious hole was discovered in a Soyuz spacecraft attached to the International Space Station.
And so on Tuesday the 2-millimeter hole led to a foot-long gash, as Kononenko sawed through the debris shield and insulation, looking for clues.
In the 7 hour 45 minute expedition, the cosmonauts took extensive photos of the drilling site and collected material from around the hole to be sent back to the Earth for testing.
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Kononenko arrived at the ISS on a Soyuz MS-11 spacecraft last Tuesday, along with NASA's Anne McClain and the Canadian Space Agency's David Saint-Jacques, weeks after the previous launch had to be aborted shortly after takeoff.
Russian cosmonauts Oleg Kononenko and Sergei Prokopyev embarked at 1559GMT (10:59 a.m. EST) for what it is expected to be a six-hour spacewalk to inspect the Soyuz's outer surface. They were also not fired by Rogozin, did not preclude that a member of the ISS crew could have drilled the hole.
The hole caused speculation about sabotage in Russian media, The New York Times reported Monday, but NASA and Roscosmos held off on elaborating further until the investigation is completed.
NASA said the pieces of freed insulation posed no threat to the space station and would likely burn up in the atmosphere in a day or so.
The Russian space agency is reportedly still in the midst of its investigation into the hole and its origins.
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Russian cosmonauts Oleg Kononenko (in the spacesuit with red stripes) and Sergey Prokopyev (with blue stripes), both Expedition 57 flight engineers, cut into the exterior insulation of the Soyuz MS-09 spacecraft during a December 11.
Head of Russia's State Space Corporation Roscosmos Dmitry Rogozin stated in early October that a commission investigating the appearance of the hole ruled out a manufacturing flaw as the cause of the incident.
Astronauts were unsure how the hole got there but plugged it using a bit of cloth and epoxy sealant.
Back in August, astronauts noticed a slight drop in pressure on the International Space Station.
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