The plane carrying the remaining seven Swedes who had been in custody in Israel arrived in Istanbul at around 3am on Thursday morning and Bildt and embassy staff were on hand to help.
"There were a lot of practical issues about baggage, things which had been taken from them, and then the onward journey home, but we also had a chance to talk about it and what they had been through," Bildt wrote on his blog, Alla Dessa Dagar.
The foreign minister praised the Turkish authorities for their work in bringing the Swedes home.
"We can thank the close cooperation with the Turkish government for the fact that it has gone fast. We have very positive and close links.
But Bildt warned that the issue remains a long way from a resolution and much remained to be done.
"First and foremost their possessions need to be returned, but then the political takes over. I will first open a dialogue with my foreign ministry colleagues around Europe over the demands which must be made for an independent investigation."
The issue is set to be raise at the upcoming meeting of foreign ministers in Luxembourg on June 14th, Bildt said adding that the discussion will lead to the larger question of the blockade of Gaza.
Carl Bildt declined to clarify whether sanctions were planned against Israel following the attacks on the convoy which have so far claimed nine lives, with dozens more injured.
"Israel has been hit pretty hard by what has happened. They have created themselves a massive political problem - their key relationship with Turkey is in the balance, as well as relations with the EU," Bildt said.