The foreign minister has, according to the Dagens Nyheter (DN) daily agreed to a meeting after coming in for criticism over his handling of the case.
Persson and Schibbye were arrested on July 1st and were found guilty of terror crimes by an Ethiopian court on Wednesday. Prosecutors have called for a maximum sentence of over 18 years in prison and are set to announce their decision on December 27th.
Bildt's predecessor as foreign minister, Social Democrat Jan Eliasson, criticized Bildt for comments made after the Swedes were arrested suggesting the two shouldn't have been in the area in the first place.
Questions have also been raised over Bildt's handling of the case in light of claims by the journalists that they were in Ethiopia working on a story about Lundin Petroleum, the board of which Bildt was member prior to becoming foreign minister.
According to Sweden's ambassador in Ethiopia, Jens Odlander, part of the reason for Sweden's "quiet diplomacy" is that the Ethiopian government refused to hold talks with Swedish representatives during the journalists' trial.
"But as soon as the verdict came, we've jump started the political process to get the Swede's free," Fredrik Spik, consular head of the Swedish embassy in Ethiopia, told DN.