Foreign ministers from the EU countries are meeting in Brussels on Friday to discuss possible military aid.
The official position of Sweden's governing centre-right alliance ahead of Friday's meeting is so far unclear.
Foreign Minister Carl Bildt advotates for humanitarian aid, and Bildt writes on his blog that Sweden has "incredibly rigorous regulations when it comes to weapons exports, and areas of conflict are almost by definition excluded."
However, the Liberal spokesperson on foreign policy, Fredrik Malm, wants to allow Swedish weapons exports, should Sweden receive a formal request from the regional government. This to avoid a genocide, he tells Radio Sweden.
"The US and other countries are helping the Kurds militarily and we should do the same in order to prevent a genocide being committed."
Within the red-green opposition, the Green Party and the Left Party are against exporting weapons to Iraq, while the Social Democrats have not yet made any statement.
The Parliament's Committee on European Affairs has to agree on a common Swedish position on the issue on Friday morning, before the meeting in Brussels.
Different opinions on how to handle the situation in Iraq is also hampering the UN Security Council, Carl Bildt and Prime Minister Fredrik Reinfeldt, both from the governing Moderate Party, argued in a debate article in newspaper Svenska Dagbladet on Thursday.
Reinfeldt and Bildt call for a unified strategy on Iraq from the UN Security Council on how to restore a lawful and democratic governance over the territories conquered by the Islamic State group.
They also want to see a representative government in Bagdad, and say that it is important to form a government as soon as possible, following the elections in April.