The report, released on Thursday, said that 29 cyclists were killed on Swiss roads in 2014, while 890 were seriously injured.
The total is the same as in 2001, which is a “dramatic” development given that road accidents overall have declined since then, the report said.
Serious accidents involving electric bicycles rose to a new high with five deaths and 145 injuries, the BFU said.
E-bikes have become an increasingly popular form of alternative transportation in Switzerland.
Accidents have risen in the past four years in direct proportion to the increase in electric bikes on the road, the report said.
The relatively high speed of e-bikes results in longer stopping distances and leads to other road users misjudging their speed, BFU spokesman Daniel Menna told the SDA news agency.
Menna said cyclists generally face considerable safety deficits.
“High-speed, built up areas and lack of (cycling) infrastructure increase the risk of accidents,” he said.
More cycling paths could reduce risks, Menna said.
The BFU is also proposing that children be systematically accompanied when they are on bikes.
The group's report shows that physical vulnerability of cyclists increases with age.
The likelihood of cyclists over the age of 64 dying in a road accident are around seven times higher than those under the age of 18, it said.
Around two-thirds of serious cycling accidents involved collisions with other road users, who were solely responsible for the incidents in more than half of the cases, according to statistics collected from 2011 to 2014.
Cycling accidents declined in the canton of Ticino, where helmet use has increased, the BFU said.
Around 43 percent of cyclists in Switzerland wear helmets, a figure that could be improved, the safety group said.
Under Swiss law, wearing a helmet is not mandatory for bicycle users.