Formally, Bildt was in the capital city, Addis Ababa, to take part in an international conference.
But while there, he spoke with Zelawi about Johan Persson and Martin Schibbye, who in December were sentenced to 11 months imprisonment for illegally entering Ethiopia and supporting terrorist groups.
"The prime minister knows our opinion very well," Bildt told Swedish Radio News after the meeting.
"That has been made clear at various meetings. We met him in February with prime minister Reinfeldt," Bildt said.
Thursday's talks are believed to pave the way for an pardon appeal to the Ethiopian government, though Bildt said he would not speculate when the Swedes may be freed.
Swedish National Radio reports that Bildt visited the journalists Persson and Schibbye at the prison where they are being kept in Addis Ababa.
In a press conference on Friday, he said that despite the difficult circumstances under which they are living, the two Swedes are in a relatively decent condition. He has still not commented on whether his visit to Eithiopia will pave the way for negotiations of their release.
"I do not dare to make a prognosis. We'll have a solution when they are freed and they are not free yet," Bildt said.
Persson and Schibbye travelled to Ethiopia to report from the conflict-ridden Ogaden province.
Shortly after entering the country embedded with the rebel group ONLF, they were captured by Ethiopian forces.