There's real concern about expatriates in Libya. Sweden has around 40 to 50 Swedes settled in the country. Bildt said that they were fully occupied with the task of helping those who wanted to leave.
The foreign minister himself will spend two days of intense talks in Cairo looking at ways Sweden and the EU can help develop the democratisation process in Egypt.
Earlier on Monday, writing about the developing violent situation in Libya in his blog, Bildt said that it is "not at all unthinkable" that the regime in Libya will collapse and that the Mediterranean EU countries are very worried about the implications of this.
That a collapse could produce many refugees is "certainly a very tangible possibility, and it will put demands on European solidarity". But, he added, "of course none of this will affect our view on the grave abuse and widespread use of violence that we are now witnessing".
Colonel Gaddafi warned the EU last week that it would stop co-operating on illegal migration if the EU backed anti-government protesters in Libya.
Sweden's EU Home Affairs Commissioner Cecilia Malmström said "Frontex experts (the EU's border agency) will assist in debriefing and interviewing migrants. Special attention is given to identifying those who may be in need of international protection. Frontex will also give aerial and naval support for border surveillance, " Malmström said.