"The Hungarian ambassador was called in Libya on Thursday and was given the message that Libya is going to suspend cooperation with the EU on immigration issues if the EU keeps making statements in support of Libyan pro-democracy protests," EU foreign policy chief Catherine Ashton said.
Hungary sits as president in the bloc's rotating presidency.
But an unnamed senior EU diplomat said the Gadhafi government is possibly holding on by a thread and no longer able to hold anything over Brussels, EUobserver.com reported Monday
"Last week, they were still capable of this kind of pressure. But today, the government is fighting for its life. It's in no position to be blackmailing anybody," the official said.
However, Rome is urging the EU to raise its alert level and send in an armed Rapid Border Intervention Team to turn back attempts at entering Europe via the Mediterranean.
Ashton had expressed "extreme concern" about the situation, while Italian officials said they didn't want to "disturb" the Libyan leader. But the Czech Republic's foreign minister, Karel Schwarzenberg, backpedaled on his earlier warning of a pro-government "catastrophe" if Gadhafi fell from power.
"I did not say that the fall of Gadhafi would be a 'catastrophe,'" he told reporters in Brussels. "On the contrary, I would think that if a wiser regime came to power, it would be profitable for the people, but right now, I do not know what the end result of the current events will be."
Ashton Sunday condemned the crackdown in Libya, which Human Rights Watch said killed 233 people during the last five days.
"The European Union is extremely concerned about the events unfolding in Libya and the reported deaths of a very high number of demonstrators," Ashton said.
France's minister to Europe, Laurent Wauquieze, said: "There should not be any state blackmail. And it is clear that Europe will not stop expressing itself."