Father-of-three, Martin O'Rourke, 24, died after he was shot several times outside a pub in the Sheriff Street/Oriel Street area at about 12:30 local time on Thursday.
It is understood the murder was a case of mistaken identity.
A handgun was found in a bin a short time after the shooting.
Mr O'Rourke tried to run but was shot several times by a gunman dressed in dark clothes, who then cycled away.
The gun is now undergoing ballistic tests but is believed to be the murder weapon. Police have also recovered a black bicycle.
The scene of the shooting remains cordoned off.
RTÃ‰ reports that it is the fifth murder as part of a feud between associates of Gary Hutch, who was shot dead in Spain last year, and David Byrne, who was connected to the Kinahan international drugs cartel based in Spain.

Five others were injured in Monday evening's blast at the Eagle Fireworks factory in Sangli district.
It was not immediately clear how the fire started.
Accidental explosions are common at Indian fireworks factories, which provide fireworks for weddings, festivals and other ceremonies.
In 2012, 34 people were killed and 30 others injured in a massive blaze at a fireworks factory in the southern Tamil Nadu state.
The BBC Hindi's Devidas Deshpande in Pune says that the latest explosion in Kavathe Ekand village was so powerful that it was heard at least five kilometres away, and the debris of the factory was scattered far and wide.
The mother and the son of the factory owner were among the dead, while his brother and three workers were seriously injured.
The village has many households making firecrackers for local religious festivals and such incidents have been reported before.
Some 25 people have been killed in at least six such incidents in the village in the past few years, our correspondent says.

F-35 air operations were paused at an Arizona air base after pilots suffered symptoms resembling hypoxia, or oxygen deprivation, Captain Mark Graff said.
Lockheed Martin, which built the jet, said it still plans to show the plane at the Paris Air Show this month.
Air Force officials said F-35 fighter jets at other bases were still in use.
Luke Air Force Base, located northwest of Phoenix, cancelled local flying operations for its F-35A Lightning II aircraft on Friday after five incidents were reported in which pilots experienced hypoxia-like symptoms.
But they continued to be grounded on Monday as the Air Force investigated the issue with pilots, maintenance workers and medical professionals, according to base spokeswoman Major Rebecca Heyse.
The incidents took place between 2 May and Thursday, but in each case the jet's backup oxygen system was successful and the aircraft landed safely.
Luke Air Force Base has 55 F-35A Lightning II jets in operation and conducts 25 training flights each weekday, according to base officials.
More than 220 operational F-35 jets have been built worldwide. The stealthy jets have logged more than 95,000 flight hours, but the planes have yet to see combat.
Police in the Republic of Ireland believe they have recovered the weapon used in the murder of a man in Dublin.
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At least nine people have been killed in an explosion at a fireworks factory in the western Indian state of Maharashtra, police say.
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The US Air Force has grounded a fleet of F-35 fighter jets indefinitely over concerns over pilots' oxygen supplies, according to a spokesman.