"All reasons to be extremely concerned over Libya. Regime violence causing high number of deaths. Completely unacceptable," Bildt wrote on his Twitter account on Sunday.
At the same time, the Swedish foreign ministry issued a statement on Sunday advising Swedes to avoid all travel to Libya.
"In light of the security situation, the foreign ministry advises for the time being against all travel to Libya," the ministry said in a statement.
The ministry, which just a day earlier had cautioned only against all non-essential travel to Libya, also said it was "urging Swedes with no pressing reason to stay to leave the country if the security situation allows."
The warnings come amid reports of a violent crackdown by Libyan security forces against protesters who began demonstrating last week against the rule of Colonel Muammar Qaddafi.
According to Human Rights Watch, more than 230 people have been killed in recent days, many in the town of Benghazi, where government forces reportedly fired with machine guns on a funeral procession.
Protests began in Benghazi on Tuesday of last week, with thousands of people taking to the streets to demand the release of a human rights advocate.
On Thursday, protests spread to other parts of the country on what was called a "Day of Rage" against Qaddafi's more than 40-year-rule.
Writing on his blog on Monday, Bildt called the weekend's developments in Libya "extremely worrying."
"A total breakdown in Libya isn't at all unthinkable and would have grave consequences in a number of different areas," wrote Bildt.
"In the Mediterranean countries, concern for what it may mean is great. A massive flood of refugees, is, at the moment, a very real possibility and will place demands on European solidarity."
In Brussels for a meeting with his European counterparts, Bildt said that he and other EU foreign ministers "strongly condemn the violence which has been used against peaceful demonstrators."
He theorised that the Libyan government appeared to have "lost a significant amount of control" of parts of the country, adding that a "peaceful development" similar to what occurred recently in conjunction with pro-democracy demonstrations in Egypt and Tunisia now appears "less likely" in Libya.
In addition to advising against travel to Libya, the Swedish foreign ministry has also advised that Swedes avoid all non-essential travel to Bahrain after anti-government demonstrators were also met with a violent response from government forces.