The president of a Swiss fine art museum has described the anguish surrounding its decision to accept a collection of modernist masterpieces bequeathed by the son of a Nazi-era art dealer.

Christoph Schäublin said it had “triggered no feelings of triumph” that the of the Kunstmuseum Bern was to take on the artworks that were recently discovered in the home of German recluse Cornelius Gurlitt.

The museum chief’s remarks followed an agreement signed in Berlin on Monday between Germany and Switzerland which will see Bern taking on several hundred works from the collection – much of which works amassed during the Nazi era and included paintings and drawings by Marc Chagall, Claude Monet and Pablo Picasso.

But under the agreement, works whose owners have yet to be identified will be left in Germany until their provenance has been traced.

Schäublin said he had not wanted to risk his museum’s good reputation and emphasised that central to the agreement was a guarantee that “looted art or works … suspected of being stolen by the Nazis will stay in Germany”.

Gurlitt, who died in May aged 81, had bequeathed his entire collection to the Kunstmuseum Bern, Switzerland’s oldest art museum.

The collection was discovered in his Munich flat in February 2012. It was confiscated by the Bavarian authorities and was at the centre of legal wranglings because of the works taken illegally by the Nazis. Gurlitt’s father, Hildebrandt, was an art dealer who was allowed to buy and sell works classified as “degenerate” by the Nazis.

Following its transition to Bern, the collection is expected to go on display to the public as early as next year.

Matisse’s Femme Assise, or Seated Woman. Photograph: Getty Images

Germany’s culture minister, Monika Grütters expressed relief at the deal signed on Monday, describing it as “a milestone in our attempts to come to terms with our history” of the Third Reich. She said Germany’s “special responsibility” had both a legal and a moral dimension that included returning illegally obtained works.

Grütters said three works that had been identified by a specialist taskforce as looted art would be returned to their owners without delay. Henri Matisse’s Seated Woman, from 1921, would be returned to the heirs of the French collector Paul Rosenberg, and Max Liebermann’s Two Riders on the Beach, from 1901, would go to the descendant of the art dealer David Friedman. A third work, a sketch by Carl Spitzweg depicting a couple playing music, was revealed on Sunday to have been identified as a looted artwork

Hildebrandt Gurlitt had purchased the work below value from the Hamburg-based Jewish publisher Henri Hinrichsen, who later died in Auschwitz in 1942. The publisher’s US-based niece Martha Hinrichsen has been informed of the decision.

The Bern museum’s decision to accept the paintings was welcomed by lawyer Chris Marinello, who represents Rosenberg’s heirs. He said the “bleak alternative” would have been to go through numerous probate courts while distant relatives of Gurlitt made their claims on the collection.

But Bavaria’s justice minister, Winfried Bausback, also a signatory to the agreement, criticised the “legal hurdles” still posed by Germany’s restitution laws which he said had often made it difficult for rightful owners to reclaim looted works after the statute of limitations had expired.

“What happens if a new collection of looted art suddenly turns up?” he said. “We found a solution for Gurlitt, but there’s no legal mechanism to deal with any similar situations in the future.”

On Friday Gurlitt’s cousin Uta Werner filed an inheritance claim with a Munich court, supported by further relatives. They claim that there are reasonable doubts as to whether Gurlitt was in a fit state of mind when he bequeathed his collection to the Bern museum. Ekkehart Gurlitt, a great cousin, told Bunte magazine that the collection belonged to Germany rather than the “small-town province” of Bern.

According to a report commissioned by the relatives, Cornelius Gurlitt had a “paranoid fear” that a network of German Nazis were trying to get their hands on his artworks. The Munich court has yet to state how it will deal with the inheritance claim.

But the director of the Kunstmuseum, Matthias Frehner, said on Monday that Gurlitt’s bequest was not as arbitrary as it might at first appear. As a child, Gurlitt had regularly visited the museum because a cousin of his father’s with Jewish roots had been forced to take refuge there during the Nazi era.

“He spent a lot of his youth in Bern,” Frehner said. “As we have since been able to piece together, it was relatively early on that he considered giving his works to us.”

Kunstmuseum Bern has a sizeable collection of modern masterpieces, including works by Paul Cézanne, Paul Klee, Wassily Kandinsky, Ernst Ludwig Kirchner, as well as Monet and Picasso.

Asked to rank the significance of the Gurlitt collection to his museum, Frehner said it was merely the “fifth or sixth most important” donation.