TRIPOLI, Libya — Col. Muammar el-Qaddafi remained at large Monday morning, and loyalist forces still held pockets of the city, stubbornly resisting the rebels’ efforts to establish full control after their astonishingly speedy advance into the capital appeared to signal the end of the Libyan leader’s four-decade grip on power.

“We do not know if he is inside or outside Libya,” Mustafa Abdel-Jalil, the chairman of the rebel government, the National Transitional Council, said of Colonel Qaddafi at a news conference in Benghazi, up until now the de facto rebel capital. He acknowledged, too, that the area of Tripoli around Colonel Qaddafi’s compound, Bab al-Aziziya, was not under rebel control.

Explosions and the sound of mortars could still be heard Monday morning, and a rebel fighter told Al Jazeera television that pro-Qaddafi forces still controlled 15 to 20 percent of the capital. An elite rebel brigade that was supposed to establish a police presence throughout the city instead found itself involved in a firefight with pro-Qaddafi forces.

News reports quoting rebel officials said tanks had emerged from Colonel Qaddafi’s compound and opened fire. “There haven’t been many silent minutes,” Karen Graham, a British nurse in Tripoli told the BBC.

But as rebel leaders said they had arrested three sons of Colonel Qaddafi, the European Union said on Monday that it had begun planning for a post-Qaddafi era. Financial markets rose smartly in Europe and the United States, and oil prices declined early on the expectation of increased Libyan production, but firmed later in the day.

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