Two men were seen "acting suspiciously" just before a blaze which caused severe damage to a mid-terraced property in Birkenhead.
The arson attack happened in Rodney Street, near the town centre, in the early hours of last Tuesday.
Merseyside Fire & Rescue Service and Merseyside Police were called to the scene at just after 1am to a report the building was on fire.
The residents of a nearby property temporarily left their house due to smoke damage.
It was reported two males had been seen acting suspiciously after getting out of a car on the road just after 12.45am, before returning to the vehicle a short time later.
The car then left in the direction of nearby Helena Street.
The house was unoccupied at the time and there are no reports of anyone being harmed, but damage was caused to the living room.
A joint police and fire service investigation is ongoing.
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Detective Inspector Tara Denn said: "Thankfully there were no injuries caused during this incident, and the fire was put out before it could spread, but the consequences could have been a lot worse for neighbours in adjacent properties.
"We are treating it as a targeted incident and have spoken to witnesses at the scene and studying CCTV footage in the area to establish exactly what happened and who is responsible.
"If you saw two males acting suspiciously in the area of Rodney Street between 12.40-12.50am, please come forward and we will take action.
"Check any home CCTV too as this may provide significant information, and if you were driving in the area please taken a look at any dashcam you may have at that time.
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"We are determined to find those responsible for putting our communities at risk and bring them to justice."
Anyone with information is asked to contact Merseyside Police social media desk via Twitter @MerPolCC or Facebook 'Merseyside Police Contact Centre'.
You can also call 101 quoting incident reference 20000557325, or contact the independent charity Crimestoppers anonymously, on 0800 555 111 or via their online form here.