In a poll carried out by the Demoskop polling firm and published on Friday in the Expressen newspaper, the Sweden Democrats were shown to have support of 9 percent of Swedish voters, an increase of 1.9 percent compared to results from the previous month.
Two weeks ago, another poll carried out by the Ipsos research firm also found the Sweden Democrats to be the country's third-largest political party amid an effort by party leader Jimmie Åkesson to rid the party of the image that its members are a bunch of "angry young men".
The recent Sweden Democrat poll surge doesn't sit well with Bildt, who expressed concerns about what the far-right party's advance might mean for Sweden.
"They are trying to isolate Sweden from the rest of the world. That can't happen," he told Expressen.
According to Bildt, the Sweden Democrats have "no other solutions" other than isolationist policies that would "cause serious damage to Sweden".
Support for Bildt's own Moderate Party dropped by 1.6 percent in the Demoskop poll, landing at 30.3 percent.
Meanwhile, support for the Social Democrats crept up 0.5 percent to 33.1 percent, allowing it to maintain its claim as Sweden's largest political party.
Overall support for the four parties of the centre-right Alliance government dropped 1.6 percent to 44.3 percent, while support for the three centre-left opposition parties fell 0.5 percent to 45.7 percent.
And while support for the Christian Democrats rose 0.8 percent to 3.7 percent, the party remains below the threshold required to maintain representation in the Riksdag.
Among several factors cited by political scientist Tommy Möller as contributing to the rise of the Sweden Democrats, was the fact that more voters now view the far-right, anti-immigrant party as "a legitimate party".
Party leader Åkesson said the immigration policies of the Alliance government have "played into our hands".
"Immigration has been quite high during the entire centre-right governing period," he told Expressen.
Earlier this week, Prime Minister Fredrik Reinfeldt attacked the Sweden Democrats as a being nothing more than internet-based provocateurs "dressed up in suits".
The Demoskop findings were based on responses from 1,003 people who were asked, "Which party would you vote for if the election were today?"