Spain and Croatia stayed top of Group A while Germany, France and Hungary are neck-and-neck in Group B after the second round of handball matches.
Spain, bronze medallists at the past two Olympics, beat Iceland 31-23 to continue their run and Croatia edged out Slovenia 27-26.
In the evening session, European champions Germany beat Egypt 26-14.
Hungary came through a tight encounter with Brazil 20-19 while France saw off hosts Greece 29-25.
Despite the scoreline, Spain had to battle hard against a determined Iceland side who trailed by only a single point at half-time.
But Spanish goalkeeper Jose Hombrados insisted his side remained among the title favourites.
"We are getting stronger and we will keep on improving
ourselves as the tournament progresses," said Hombrados.
In the other group A match Yoon Kyun-shin and Lee Jae-woo grabbed seven goals apiece for South Korea as they beat Russia 35-32.