Swedish and Danish authorities have been investigating four leaks from the pipelines in Swedish and Danish exclusive economic zones in the Baltic Sea since they were first spotted at the beginning of last week.
Europe, which is a facing an energy crisis is investigating what caused the damage as Moscow seeks to pin the blame on the West, suggesting the United States stood to gain.
Washington denies any involvement as a stand-off between Russia and European countries continues over supplies of gas that have stopped flowing or been put on hold as a result of the conflict in Ukraine.
The Nord Stream operators said this week they were unable to inspect the damaged sections because of restrictions imposed by Danish and Swedish authorities who had cordoned off the area.
"After completing the crime scene investigation, the Swedish Security Service can conclude that there have been detonations at Nord Stream 1 and 2 in the Swedish economic zone," the Swedish Security Service said in a statement.
The security service said there was extensive damage to the gas pipelines and they had retrieved some material from the site that would now be analyzed. The evidence has strengthened the suspicions of gross sabotage, they said.
Sweden's Prosecution Authority said in a separate statement that the area, where gas spewed into the sea for almost a week, was no longer cordoned off.
Russia said on Thursday it had been informed via diplomatic channels that it was not able to join the investigation.
"As of now, there are no plans to ask the Russian side to join investigations," Kremlin spokesman Dmitry Peskov told reporters, adding that Moscow replied it was not possible to conduct an objective investigation without its participation.
Swedish prosecutors had on Monday cordoned off the area of the leaks for a crime scene investigation conducted by the Swedish Coast Guard and Navy.
On Wednesday, Sweden's Justice Minister said in response to the Kremlin that it was not possible to let others take part in a Swedish criminal investigation.
Denmark's Foreign Minister Jeppe Kofod told Reuters on Thursday that his Ministry had not told Russia to stay out of the investigation, but that a police-led taskforce between Denmark, Sweden and Germany was in charge of the investigation.
Maria Zakharova, spokeswoman for the Russian Foreign Ministry, said separately on Thursday that Moscow would insist on a comprehensive and open investigation that includes Russian officials and Gazprom.
"Not to allow the owner (of the pipelines) to witness the investigation means there is something to hide," Zakharova said.
