Father and son Kuznetjik climbed over a fence at the embassy on September 11.
Their purpose was to seek asylum in Sweden, but were instead informed that the embassy does not accept asylum applications.
It is only possible to submit an asylum application to a border police or at one of the Swedish Migration Board's application units.
And the men have been at the embassy since then, where they have received food and drink, according to previous information from the Ministry of Foreign Affairs.
According to the Swedish Ministry of Foreign Affairs, the two men Vladislav and Vitaly Kuznetjik were still at the Swedish embassy in Minsk on Saturday.
"An important human rights issue"
After the men have made an application to the European Court, the court is now considering trying the case.
Therefore, the court has asked Sweden about the government's possible measures regarding men.
Lawyer Percy Bratt, an expert on human rights, believes that there is a good chance that the European Court of Justice will take up the case.
- It is an important human rights issue that is illustrated here.
What responsibility do you have when people who are threatened with torture or killed escape into an embassy area?
Can you then say "we drive them out to the bloodhounds again, we have no responsibility for this?"
I think that is an important issue.
And I understand that the government is afraid of the consequences.
It is possible that the European Court of Justice will try the case
The government writes in its response that Sweden has not violated men's human rights, and argues that the case should not be considered.
This is because the Swedish embassy is not Swedish territory, and that embassies are not meant to function as "a protection for intruders".
But Percy Bratt believes that it is still possible for the European Court of Justice to try the case.
- It is precisely the case that when it comes to such hard and absolute rights, as the right not to be subjected to torture or gross inhuman treatment, then you have a very far-reaching responsibility.