Two men are being questioned over the murder of Pc David Phillips, who was mown down and killed by a driver in a stolen car.
The pair, aged 18 and 30, from the Oxton and Wallasey areas of the Wirral, were arrested in connection with the killing of the 34-year-old father of two in the early hours of Monday.
A memorial fund set up in Pc Phillips' memory has so far raised more than £45,000 from more than 2,000 donors.
On Tuesday, Merseyside Police said it had executed four warrants in the areas as part of the murder investigation into Pc Phillips' death as detectives continued to appeal for information.
Detective Chief Superintendent Paul Richardson thanked the public for its support.
He said: "Since the investigation was launched yesterday we have been inundated with calls from members of the public and as a result we are following up a number of positive lines of inquiry.
"From the hundreds of supporting and caring comments on social media and media websites yesterday, it is obvious that there is overwhelming support for the police and that the public appreciate the work undertaken by officers like Pc Phillips to keep their communities safe.
"I would like to appeal to any members of the public who have any information which could help us with the investigation to come forward."
Pc Phillips had been sent to assist following a burglary at an estate agents in Birkenhead where a red Mitsubishi pick-up vehicle was stolen just after 1am on Monday.
Following a police pursuit at about 2.08am, Pc Phillips and a colleague had attempted to use a "stinger" device to stop the runaway Mitsubishi Challenger L200.
But the car mounted a central reservation and headed directly at the officer before speeding off. Pc Phillips was given CPR by colleagues at the scene but died a short time later at Arrowe Park Hospital on the Wirral. The pick-up was later found abandoned in Corbyn Street, Wallasey.
Merseyside Police Federation Charitable Trust set up a Just Giving page to honour an officer "tragically and unlawfully killed whilst on duty".