By Ghaith Shennib and Feras Bosalum

TRIPOLI (Reuters) - Assailants attacked an Islamist party office in Tripoli on Monday and a soldier was killed in fighting in Libya's eastern city of Benghazi, officials said, in an escalation of violence following the assassination of a political activist last week.

A government source confirmed Social Affairs Minister Kamila Khamis al-Mazini had publicly announced her resignation, several days after Prime Minister Ali Zeidan promised to reshuffle his cabinet to help cope with the "urgent" situation in Libya.

"This escalation (in violence) will lead to a collapse of a whole nation. We need solidarity of the people," Zeidan told reporters in Tripoli on Monday.

"People think the state is weak but the state does not even exist," he said. "Even if you brought the best politician from America or Europe, he will find himself helpless here."

In a move to try and reassert the military's authority, Libya's national assembly selected Abdesalam Jadallah, a colonel in the special forces, as the new army chief of staff on Monday.

A former frontline rebel commander during the 2011 war, Jadallah was picked after his predecessor resigned in June following deadly clashes in Benghazi.

The spark for the latest unrest was the slaying of Abdelsalam al-Mosmary, a prominent critic of the Islamist Muslim Brotherhood movement who was gunned down as he left a mosque in the restive eastern city of Benghazi on Friday.

Protesters aimed their anger at a variety of targets over the weekend, including the Benghazi and Tripoli offices of the Brotherhood and the headquarters of a liberal coalition in the capital.

Early on Monday, an unidentified group attacked the headquarters in Tripoli of the al-Watan (Nation) political party, led by former Islamist militia leader Abdelhakim Belhadj.

"They smashed windows, shot at the door locks to open them and threw Molotov cocktails inside," Jamal Ashour, head of the party's political office, told Reuters. "The damage is serious. No one was injured."

AUTHORITY WEAK

The demonstrations have added to a sense of lawlessness in a country where the government has been unable to assert its authority across large areas following the 2011 war that toppled autocrat Muammar Gaddafi.

Militia groups who seemingly act as they please have further destabilized the oil-producing north African state, including in the eastern city of Benghazi, the cradle of the anti-Gaddafi uprising and scene of a dramatic prison break at the weekend.

More than 1,100 inmates escaped during a riot in Kuafiya prison on the outskirts of Benghazi on Saturday, and officials said on Sunday only about 100 prisoners had been recaptured.

Also on Sunday, two blasts targeted judicial buildings there, wounding 43 people, according to state news agency LANA.

Hours later, fighting erupted overnight in Benghazi's western Gwesha district.

"Clashes broke out between special forces and an unknown armed group," Mohammed al-Hijazy, a spokesman for Benghazi security operations, said by telephone. "At least one soldier was killed. The special forces have now retaken control."

Hijazy later said a military vehicle exploded in central Shajara Square. It was not immediately clear what had happened but residents said the blast was minor.

Violence has plagued Benghazi since last year, with attacks on security forces as well as foreign targets, including an assault on the U.S. mission in September in which the U.S. ambassador and three other Americans were killed.

(Additional reporting by Feras Bosalum; Writing by Marie-Louise Gumuchian; editing by Mike Collett-White)