“Let those who know what they're doing handle it,” Bildt said to TV4 on Thursday.
Bildt waved off a new motion handed in by the Greens on Thursday, proposing that it might be better if the prime minister handles the matter as “party political bickering”.
According to the Greens, not enough is being done to ensure the Swedish reporters' return to Sweden.
“The government need to step it up,” Mats Pertoft, MP for the Green Party, told TV4.
The two journalists had entered the country illegally and were in the company of the region's ONLF guerrillas at the time of their arrest.
From the beginning the pair have been adamant that they are innocent of terrorist charges.
Recently there has been speculation in the Swedish media whether the two were in the country to report on Lundin Petroleum, a Swedish oil and mining company, at the time of their arrest.
In a report from 2010, ECOS (European Coalition on Oil in Sudan), an umbrella group of European organizations published a report called "Unpaid Debt", urging Sweden, Austria and Malaysia to probe whether Lundin Petroleum (then Lundin Oil), in consortium with Petronas and OMV, had broken international law between 1997 and 2003.
Swedish foreign minister Carl Bildt was on the board of directors of Lundin Petroleum at the time.
However, on Thursday Carl Bildt rejected any claims that his previous involvement with the company would have an impact on the dealings with Ethiopia in the case of the two jailed reporters.
“Why would it? There is no conceivable reason for that. I don't believe that Lundin Petroleum is in that area but even if they were, it would be totally irrelevant,” Bildt said on Thursday.
Although the Greens don't have confirmation of a connection between the foreign minister and the area, they think that the government must take a more stern approach in the matter.
“And one way of doing that, irrespective of Carl Bildt, is to hand the issue over to the prime minister,” Pertoft said.
However, Bildt said to TV4 that he thinks it is better to let those that are dealing with the matter continue their work on it.
“At the foreign ministry, we have considerable experience in these matters. Sometimes we solve things without you even hearing about them, and other times we make use of loud diplomacy,” Bildt said on Thursday.
On Friday demonstrations are planned by the organization Reporters without Borders, the Swedish Journalists' Union and the Swedish Publishers' Association in Gothenburg and Stockholm.
The organisations demand that the government give the case the highest political priority, that Bildt and Reinfeldt officially show their support of the two Swedes and that the matter is raised internationally.