His coalition partners have rejected opposition calls for early elections and have, for now, backed Dacic, a once-close associate of late Serbian strongman Slobodan Milosevic who has become a pro-EU reformer, but have also insisted that all those who are guilty must bear the consequences.
The affair, however, leaves a question mark above the future of the ruling coalition, made up of Dacic's Socialists and reformed nationalists from the Serbian Progressive Party (SNS), which has won kudos for its crackdown on organized crime and corruption and the pragmatism of its approach to Kosovo.
In the meantime, Dacic's deputy, Aleksandar Vucic of SNS, appears to be benefiting the most from Dacic's troubles. Some now see him emerging as the most powerful politician since the overthrow of Milosevic.
Serbian media have been speculating for months about possible contacts between government officials and Montenegrin-born alleged international drug smuggler Darko Saric, who has been on the run for four years.
A month ago Dacic, who has also been interior minister since 2008, called on anyone with specific information to step forward so that police might immediately arrest officials who were in contact with Saric or his people.
On February 2, however, he stunned everyone by confirming last week's media reports that it was actually him who met, four years ago, with Saric's fellow Montenegrin and associate Rodoljub Radulovic, who goes by the nickname "Misha Banana."
In his defense, Dacic said Radulovic's name was not in the government's "White Book" on the Saric clan. He declined to say what he had discussed with Radulovic.
"Even before they used to say that I will protect this or that businessman, and where are they now? All in prison. And all of those proven guilty who I know will also go to prison. The fact that I know them is not protection but a handicap for them because I will be even more ruthless because they [will have] betrayed my trust," he said.
Some Belgrade analysts say the affair was cooked up by the opposition Democratic Party, Dacic's coalition partners until April, and specifically by those who were close to former President Boris Tadic.
"This affair was not created by Dacic but by the people who had the information and should have shared [it] so that Saric and his group could have been criminally prosecuted. They are using them and manipulating them, first of all, for political purposes," Zoran Mijatovic, a security expert and former high-ranking state security official, said.
If there is a silver lining to the Saric "affair" for Dacic, it is that it completely overshadowed an embarrassing episode from last week. Dacic was invited to an interview that turned out to be a prank staged by the "Nemoguca misija" ("Mission Impossible") television show in which he was flashed by a leggy, pantiless former Playboy model (here's the potentially offensive link) in a candid-camera-style reenactment of the famous Sharon Stone scene from the 1992 thriller "Basic Instinct."
The video of the interview, which was shelved after a public outcry, went viral with more than 5 million views and the story was picked up by media outlets around the world. A Dacic adviser characterized the seedy prank as a "mockery of Serbia, not the prime minister," and vowed that Dacic's office "will not let this go unpunished."
-- Nedim Dervisbegovic, with reporting by RFE/RL's Belgrade bureau