Pc David Phillips "did not stand a chance" when the vehicle drove directly at him in Wallasey, Wirral, his chief constable said.
Sir Jon Murphy admitted police had "no idea" who was responsible for the tragedy, but warned the culprits: "We will find you."
Pc Phillips was standing on a central reservation when the Mitsubishi mounted the kerb and hit him at speed before driving off.
The stolen vehicle was found abandoned nearby a short time later, Merseyside Police said.
Donna Allen, a Superintendent for Greater Manchester Police offered prayers for the officer online.
"Thoughts & prayers this morning after hearing the tragic news of an officer killed in Merseyside last night," she said.
Chief Superintendent Sally Bourner from West Midlands Police said: "Awful news - sending thoughts & prayers to family, friends and Merseyside Police colleagues".
The 34-year-old officer was with a young colleague who tried to stop the stolen vehicle using a stinger device to puncture its tyres.
"The Mitsubishi vehicle mounted the central reservation, drove directly at the officers down the central reservation and hit Constable Phillips. He did not stand a chance," Sir Jon Murphy said.
Pc Phillips was married and he and his wife, Jen, had two girls, Abigail, aged seven, and three-year-old Sophie.
He joined Merseyside Police in 2006 and was "popular and held in high regard" by his colleagues.
Sir Jon said Pc Phillips is the first Merseyside Police officer to be killed on duty as a result of a criminal act since 1981 and paid tribute to the bravery of his officers.
Merseyside police and crime commissioner Jane Kennedy's voice broke with emotion as she spoke to dozens of TV crews, reporters and photographers at the press conference at the force HQ in Liverpool.
She said: "Police officers are on the front line every single day protecting our communities.
"It's a dark day when you lose one of our own and it's a painful reminder of the risks police officers face to keep us all safe."
Peter Singleton, chairman of Merseyside Police Federation, said Pc Phillips' colleagues are "understandably devastated", adding: "When any officer is killed on duty it is a tragedy and in Dave's case it is possibly more so. His young children have been robbed of a father, his wife Jen, deprived of a husband and his parents, their son.
"His colleagues and friends have (lost) a respected and truly exceptional officer.
"He was one of the best and will always be missed."