"We must be at the absolute cutting edge in digital diplomacy efforts," Bildt said in his Wednesday address to the Swedish Riksdag.
He promised that all Swedish embassies would be tweeting and sharing information on Facebook by the end of February.
Bildt noted that Swedes travelling abroad was growing ever more frequent. Since 2009, trips abroad had increased by 25 percent - hitting a total in 2012 of 15 million visits to other countries.
He said a digital presence would allow the foreign ministry to master "new tools to meet the growing consular challenge."
Sweden previously established an embassy in the virtual world Second Life, a move that garnered headlines across the world.
The foreign ministry in Stockholm handles about 2,000 cases a year involving Swedes abroad, he noted, while the missions abroad - embassies and councils - oversee many more.
A central task, he noted, was "to provide efficient and legally secure consular support to people in distress."
"We want a trip to be a memory for life, not a number in the foreign ministry's statistics."
Bildt often addresses the role of the internet. In 2013, Sweden will for the second year in a row host a global conference on freedom of expression online, he noted.
"Sweden is a leader in the fight for all people's rights and opportunities to communicate freely and securely on the internet," he claimed.
In his Wednesday speech, he said efforts were under way to make the EU agree on a "common cyber security strategy."
He said Sweden was also pushing for an agreement in the UN Human Rights Council to ground the same freedoms of press and expression that exist offline to the online world.
He slammed governments that sought to curtail communication.
"In negotiation after negotiation, we stand up against regimes that, for their own survival, seek to prevent freedom of expression in modern communications," he said.
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