Security official Ahmed Mohamed told The Associated Press the pirates disembarked the ship, which was heading to Bossaso port, the region's commercial hub, with its eight Sri Lankan crew members aboard.
Aid group Oceans Beyond Piracy said in a statement late on Tuesday the ship was carrying gas and fuel and was not registered with the Maritime Security Center for the Horn of Africa, which registers and tracks vessels in the region. "They made (the pirates) an offer they couldn't refuse and the pirates have left", said John Steed, a former British army officer with the NGO who has spent years negotiating the release of piracy hostages in Somalia.
A pirate who had spoken to Reuters news agency had threatened to kill the hostages if the Puntland forces continued to fire at them.
Earlier, the hijackers have claimed to be fishermen whose livelihood undermined from foreign fishing ships in Puntland waters amid growing frustration against Puntland government for granting fishing permits to foreign ships.
Officials said local elders negotiated the release of the Aris 13 and that as part of the negotiations, the pirates were allowed to leave the vessel and return to shore.
At the time the tanker was taken it was forced to change course and head toward Puntland.
The Monday hijack was the first such attack near the Somali coast since 2012. Somali maritime police attempted to intercept a boat that was carrying supplies to the pirates but were fired at by the hijackers.
Residents near the ship in the semi autonomous region of Puntland reported hearing gunfire.
A U.N. shipping database shows the Aris 13 is owned by Armi Shipping SA, whose address is listed in care of Aurora Ship Management FZE, a company based in the United Arab Emirates.
The gunmen are demanding a ransom to release the ship and its Sri Lankan crew, said the EU Naval Force. The ships tracking system has reportedly been switched off.
Somali pirates began staging waves of attacks in 2005, seriously disrupting a major worldwide shipping route and costing the global economy billions of dollars.
Pirates argued that they are fighting illegal ships and boats which are collecting their natural resources, mainly the fish.