A French investigation into the causes of the 1994 Rwandan genocide has exonerated the president, Paul Kagame, and his Tutsi allies after Paris had previously accused him of triggering the killings of 800,000 people in 100 days.

Diplomatic relations between Rwanda and France were broken off in 2006 when a French judge said that Kagame – the rebel leader at the time of the killings – had orchestrated the assassination of the Hutu president, Juvenal Habyarimana, to trigger the bloodshed.

After Habyarimana’s plane was shot down, Hutu extremists slaughtered Tutsis and moderate Hutus in some of the fastest mass killings ever perpetrated.

Kagame’s Tutsi-led Rwandan Patriotic Front seized power in the aftermath of the genocide.

Kagame has accused the former French president François Mitterrand’s administration of training and arming the Hutu militias responsible for the slaughter.

A team of French investigators, led by two judges, re-examined a dozen eyewitness testimonies to work out where the two missiles that brought down Habyarimana’s Dassault Falcon 50 plane were fired from in an effort to determine final responsibility. Both sides had bases near the airport.

On Tuesday, the judges presented their report to Kagame’s lawyers, who told the media they had concluded that the shots could not have come from a military base occupied by Kagame’s supporters. The findings did not specifically point the finger at the Hutus.

“Today’s findings constitute vindication for Rwanda’s long-held position on the circumstances surrounding events of April 1994”, the Rwandan foreign minister, Louise Mushikiwabo, said in a statement.

“With this scientific truth, [the judges] have slammed shut the door on the 17-year campaign to deny the genocide or blame its victims.

“It is now clear to all that the downing of the plane was a coup d’état carried by extremist Hutu elements and their advisers who controlled Kanombe barracks.”

However, Jean-Yves Dupeux, a lawyer for Habyarimana’s children, said the findings did not support the Rwandan government’s account.

“The findings cannot point the finger at the Hutu camp,” he added. “What the experts are saying is that the shots could not have been fired from Paul Kagame’s camp. That doesn’t mean it is the other side.”

An investigation by the Rwandan government in January 2010 blamed extremists within Habyarimana’s inner circle for bringing down the plane, saying the murder was designed to scuttle a planned power-sharing deal and act as a pretext for the genocide.

According to the Rwandan inquiry set up by Kagame – known as the Mutsinzi report – Rwanda armed forces stationed in the Kanombe barracks near the airport fired the surface-to-air rockets, the culmination of months of planning.

A 2006 report by the French judge Jean-Louis Bruguiere said Kagame was responsible, arranging for the plane to be shot down to trigger reprisal killings between ethnic Tutsi and Hutu and give his RPF rebels and allies grounds to take power by force.

Paris began to normalise its relations with Rwanda after Nicolas Sarkozy came to power in 2007. On a trip to Kigali in February 2010, the French president said Paris had made serious errors of judgment over the massacre and wanted to ensure that all those responsible for the slaughter were caught and punished.

On Kagame’s first state visit to France since the genocide in September, the Rwandan president emphasised that his trip was aimed at building economic and commercial ties, appearing to accept that an apology from Paris was no longer a prerequisite for restoring diplomatic ties.