"Crimea is a not question for Nato," Bildt told Sveriges Radio (SR). "Of course I am worried, but I am more worried about the financial situation and the corruption."
(Please note that The Local misreported Bildt's comment as saying he thought Nato should consider keeping an eye on Crimea.)
Reports came in on Friday of unidentified armed military blocking access to the Sevastopol and Simferopol airports in the Ukrainian region of Crimea. Ukraine's new interior minister, Arsen Avakov, claimed the airports had been taken over by Russian soldiers. Crimea, Ukraine's only region that is populated by a Russian majority, is now playing host to a face-off between those loyal to Russia and those supporting Ukraine's new leadership.
Russian and Ukrainian relations have been tense since Ukrainian President Viktor Yanukovych fled Kiev in the wake of a deadly crackdown on protesters.
Bildt tweeted that the news organization Russia Today had published quite a level-headed analysis of the situation.
In the piece, the Crimean peninsula was described as "a crossroads of cultures – and a hotbed of conflicts". Bildt called it a "difficult place", in an interview with Aftonbladet.
"It's a potentially explosive situation, so I think it is in everyone's best interest to deal with this cautiously," he added.
As for the situation at large in Ukraine, Bildt on February 27th blogged that the country had a "golden opportunity" to move forward. He pinned his hopes to new Prime Minister Arseniy Yatsenyuk, who, Bildt wrote, "has himself talked about the job of leading the government as a 'Kamikaze Mission'."
"I remember discussions with him not that long ago about the economic reform that will be necessary but also the political risks these can entail," Bildt wrote.
He concluded that reform was possible, but "it will demand both political clout and financial support".
"The EU will be the deciding factor in the first matter, and the IMF in the latter," he said.
This story was amended at 14:37pm on February 28th, 2014.