"The walls are closing in on the dictator's compound," he said.
"The situation can bring disastrous consequences if in the next few hours Gaddafi doesn't announce his decision surrender and turn himself in," Frattini said.
Prior to joining a UN-mandated military campaign against Gaddafi's forces in March, Italy was Libya's closest trading partner. In one trip to the North African country, Italian prime minister Silvio Belusconi kissed Gaddafi's hand.
Three of Gaddafi's sons have reportedly been captured by rebel forces who encountered little resistance when they entered the Libyan capital Tripoli on Sunday.
Libyan information minister Moussa Ibrahim told CNN government still had 65,000 loyal soldiers fighting under for Gaddafi's government while a rebel spokesman said those forces still control up to 20 percent of Tripoli.
The rebels' Transitional National Council is ready to move to Tripoli, according to Ali Suleiman Aujali, who is the rebel government's ambassador to the US.