Police in western Germany have arrested two men suspected of being involved in the killing of two police officers who were shot dead on a rural road while on a routine patrol.

The shooting happened during a traffic check near Kusel at about 4.20am on Monday, police in Kaiserslautern said.

The officers were able to radio that shots were being fired, telling colleagues “they are shooting at us,” a spokesperson, Bernhard Christian Erfort, said. But reinforcements were unable to save the officers, a 24-year-old woman and 29-year-old man.

Erfort said he did not know whether the officers had seen something particular about the assailants’ vehicle that they wanted to check or whether it was a routine stop. Both officers were wearing police uniforms and protective vests.

The officers reported finding dead game in the car before the shooting started, police have confirmed.

Police officers secure the rural road where the fatal shooting took place.

The younger officer, who was still studying at a police academy, was reportedly dead by the time reinforcements arrived, while her colleague died shortly after.

The female officer was still carrying her gun in its holster when she was found, wrote the tabloid Bild, without citing sources. The male officer had managed to fire several shots before he was killed, it said.

The perpetrators fled but police had no description of them, the car they used or in which direction they had gone.

On Monday afternoon police released a picture of a suspect, 38-year-old Andreas Johannes Schmitt, who runs a bakery and a business selling wild game in the town of Spiesen-Elversberg, in Saarland state. Investigators had reportedly found documents identifying the suspect at the scene of the crime.

At 5.30pm, the state prosecutor in Kaiserslautern announced the arrest of the previously identified suspect, as well as the arrest of another 32-year-old individual. Police were continuing to look for others possibly involved in the killing.

According to Der Spiegel, Schmitt owned a gun licence but was not previously known by the authorities for extremist tendencies.

The shooting of the two police officers has been met with shock around the country. Across Saarland state, flags were flown at half mast.

The German interior minister, Nancy Faeser, said the circumstances of the killing reminded her of “an execution”. “Irrespective of what the motive behind this deed is, this deed bears the hallmarks of an execution, and shows that police officers risk their lives for our safety every day.”