US tanks gunned Dana down as he filmed an attack on an Iraqi prison, mistaking his camera for a rocket-propelled grenade launcher.
He was the second Reuters journalist to be killed by US troops in Iraq since the war to oust the Iraqi dictator began in March.
In April, Reuters cameraman Taras Protsyuk, 35, died of the wounds he received when a US tank fired a single round at Baghdad's Palestine Hotel, which is home to much of the foreign media covering Iraq.
Calls for an inquiry were made by the Committee to Protect Journalists and Reporters Sans Frontieres in Paris.
RSF secretary general Robert Menard said: "Not only have US troops committed numerous blunders during the war but -- at this point -- these have not been the subject of an investigation worthy of the name."
He went on to criticise the US's enquiry into the shelling of the Palestine Hotel, which he said exonerated the US army in a shameful way. He called on Washington to publish its report in full.
Reuters also called on Washington to investigate the tragic killing of Dana. The 41-year-old Palestinian, who has been wounded several times previously, had been due to return home to his wife and family in Israel's West Bank.
Reuters said it also wants the killing of Ukranian Protsyuk to be probed. In that incident, US troops said they thought they had been fired on from within the hotel.
Reuters chief executive Tom Glocer said: "Coming so soon after the death of Taras Protsyuk, also killed by a US tank, this latest death is hard to bear. That's why I am personally calling upon the highest levels of the US government for a full and comprehensive investigation into this terrible tragedy."
Reuters quoted Dana's soundman Nael al-Shyoukhi, who said that the US soldiers had seen them and knew their identities.
"After we filmed we went into the car and prepared to go when a convoy led by a tank arrived and Mazen stepped out of the car to film. I followed him, and Mazen walked three to four meters. We were noted and seen clearly," Shyoukhi said.
"A soldier on the tank shot at us. I lay on the ground. I heard Mazen, and I saw him scream and touching his chest.
"I cried at the soldier, telling him you killed a journalist. They shouted at me and asked me to step back, and I said, 'I will step back but please help, please help and stop the bleed.'"
A spokesman for Amnesty International told Reuters that the high-profile deaths were increasing anti-American feelings.
Said Boumedouha, Amnesty's human rights group's Iraq researcher, said: "They're definitely taking place on a very regular basis. This is increasing the anti-American feeling."
Colonel Guy Shields, a US military spokesman, said: "Last night, we had a terrible tragedy. I can assure you no one feels worse than the soldier who fired the shots."
The death of Dana brings to 18 the number of journalists killed in Iraq, the biggest death toll of journalists in such a short period of time covering any previous war.
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