The Swedes were wounded during the gunfight, in which 15 rebels were reportedly killed.
On September 7, they were charged with being engaged in terrorist activities, aiding and abetting a terrorist group, and entering the country illegally without permission, from neighbouring Somalia.
Sweden's foreign ministry said that they had not expected the charges of terrorism, but anticipate they will be dropped.
"We were surprised and disappointed by this, because we believe in their claims to be journalists, I can't see any reason why these charges will not be dropped," Anders Jörle of the ministry's information department told AFP.
The process has already caused controversy.
Ethiopian Prime Minister Meles Zenawi told Norway's Aftenposten newspaper last week that they are "at the very least messenger boys of a terrorist organization, they are not journalists."
The comments sparked an angry condemnation from the New York-based media rights watchdog, the Committee to Protect Journalists (CPJ).
"The Ethiopian government has compromised their fundamental rights of defence, chiefly, the presumption of innocence, by portraying them in the media as accomplices to terrorists," the CPJ said in a statement.
The trial also casts rare light on Ethiopia's south-eastern impoverished Ogaden region, home to ethnic Somalis and the ONLF rebels, who have been fighting for independence from the central government since 1984.
The recent discovery of oil and gas in Ogaden has brought hopes of wealth, but also new sources of conflict, with the ONLF threatening foreign workers and the government cracking down on opposition it says are rebels.
"The Ogaden has become strategically quite important because these resources need to be exploited," said David Anderson, professor of African politics at Oxford University, adding that the region has become an "embarrassment" for the regime in Addis Ababa.
International rights groups say the Ethiopian government has already made widespread use of anti-terror legislation to crack down on suspected opponents.
The law is a "smokescreen for imposing a set of promulgations that allow the government to deal with its opponents," Anderson said, adding that it allows "an unscrupulous government to behave unscrupulously."
At least 157 people, mainly journalists and opposition members, have been arrested since May on suspicion of being connected with various outlawed groups, detentions heavily criticised by Amnesty International.
"All these arrests are just abusing the anti-terror legislation, or misusing it, to stifle freedom of expression," said Amnesty's Ethiopia researcher Claire Beston.
The Ethiopian authorities have rejected the accusations, saying the arrests are a legitimate response to a network of rebels it claims are backed by long-term foe and neighbour, Eritrean President Issaias Afeworki.
"There is a conspiracy under way that tried to animate a series of terrorist attacks all over the country," government spokesman Shimeles Kemal said.