Silvio Berlusconi, Italy's prime minister, said on Thursday the $285m cost of holding the summit on the island would be better spent on reconstruction in the quake-devastated town.
But the decision still needs the approval of other G8 nations before it can go ahead.
"What seat would be more appropriate than a land wounded by the earthquake?" Berlusconi said at a news conference in L'Aquila on Thursday.
"The 21 heads of government who come will be able to see first hand the wounds caused by this earthquake. I think it could work out very well," he said.
'Implausible' feat
Berlusconi did not elaborate on how much it would cost to host the summit in L'Aquila, but insisted it would save money.
The April 6 earthquake in Italy's Abruzzo region killed 295 people and left at least 50,000 people homeless.
Italian media have reported that the government was having difficulty organising the summit on La Maddalena, with trouble finding ships that could host delegates and journalists.
Berlusconi said L'Aquila, an hour's drive from Rome, would have enough hotels for delegates and journalists.
He said demonstrators were less likely to march on a region devastated by an earthquake than a resort on an Italian island.
But some politicians within Italy's cabinet disagreed over moving the G8 summit, with at least one minister saying it was "implausible" and difficult to pull off.
The cabinet approved earlier on Thursday $10.36bn in funding over three years to rebuild the area hit by the earthquake and support emergency services.