The victims were Amal Khalil, 53, Atef Haj, 48, and Nasif Bader, 52, all from Marar in the Galilee region of northern Israel.
One other man and four women were injured in the crash at a crossing without security barriers in the municipality of Wolfenschiessen.
Two of the three men who died were policemen, The Times of Israel reported online.
The newspaper identified Khalil as the head of the police investigations division in northern Israel, while Haj was a police investigator.
It said the wounded man was Wafa Azzam, the brother of Azzam Azzam, who served eight years in an Egyptian prison for spying on Israel.
The four Israeli couples, aged between 40 and 60, were on a holiday to explore central Switzerland — Lake Lucerne, Titlis mountain and Kapellbrücke — when the accident occurred at around 8.40am.
It is not clear why the van travelled across the tracks just as the passenger train came, but it appears the minibus was headed to a small road that leads to a waterfall, visible from the crossing.
The accident at the crossing is the second in less than three weeks and has raised safety concerns about the number of crossings without safety barriers on the narrow-gauge Zentralbahn line.
The railway acknowledged it has 70 crossings that lack barriers on its two lines that link Lucerne with Engelberg and Interlaken.
Zentralbahn’s managing director Renato Fasciati said the railway has upgraded 147 of 217 “unsecured” level crossings, the Blick newspaper reported online.
The company has focused on dealing with crossings that posed the greatest uncertainty for road users, Fasciati said.
On July 21st, the driver of a Mercedes station wagon was lucky to escape injury when a Zentralbahn train collided with the vehicle at the Wolfenschiessen crossing on July 21st.
Fasciati said all the unsecured crossings cannot be fixed immediately but he told a press conference on Monday that upgrading them “is a top priority for us — we are well on our way”.