Faizullah Muradi, 22, who worked with Norwegian forces fighting in Afghanstan, was deported to Rome on Tuesday under the so-called Dublin regulations.
The case has upset many in Norway, who argue the country should be more generous to those who risk their life in its service.
Muradi on Thursday told NRK that he was hopeful after the Prime Minister's intervention.
"I am very happy, but I know that no one is giving me a guarantee that I will get back to Norway," he told the network.
He revealed that he had spent Wednesday wandering homeless in Rome, unable to afford to buy food.
"I have neither money nor a roof over my head. It has been a cold night," he told NRK.
He will apply for asylum in the Italian city of Lecce on Thursday.
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"Norway is concerned that those who serve Norwegian forces abroad should be treated well," Solberg said announcing the review. "I therefore ask the Minister of Justice to investigate the use of the Dublin Regulation in the treatment of asylum applications from people who have had employment with Norwegian forces in Afghanistan."
"This means that you also need to consider whether the person who was recently deported should get his application processed in Norway," Solberg said.