WASHINGTON (AFP) - Washington is closely monitoring an upsurge of violence in Libya, but has not decided yet whether to order the closure of its embassy in Tripoli, a US official said on Monday.

Libyan gunmen stormed parliament in southern Tripoli on Sunday, hot on the heels of an anti-Islamist offensive launched by a rogue general in the eastern city of Benghazi.

"We remain very concerned about the violence over the weekend in Tripoli and Benghazi," State Department spokesman Jen Psaki said, calling on all sides to "refrain from violence."

While Saudi Arabia on Monday closed its embassy in Tripoli and evacuated its diplomats, Ms Psaki said: "We have made no decisions to move any of our personnel out of Libya."

The United States has been closely watching events in Libya ever since the late ambassador, Chris Stevens, and three other Americans were killed in a 2012 militant attack on a US diplomatic mission in Benghazi.

The mission, which was badly damaged in a fire, was closed in the wake of the attack, and embassy staff in Tripoli were reduced to emergency levels.

New ambassador Deborah Jones arrived in Libya in mid-2013, but tweeted on Monday that she was "on family travel. Watching #Libya with heavy heart and praying enduring solutions emerge."

"Compromise required (but #NoRoomForTerrorism)," she added in her Twitter message.

A State Department official confirmed to AFP that the ambassador had left before the weekend's unrest and that the embassy was currently operating "normally" and was not on any authorized or ordered departure.

Ms Jones, a veteran diplomat and former ambassador to Kuwait, vowed during her swearing-in last June to stand with Libya as it moves towards democracy.

"The Libyan people endured 42 years of rule by intimidation. They courageously defeated a dictator and are now determined to experience governance by representation," she said.

Ms Psaki said both President Barack Obama and Secretary of State John Kerry have been briefed on the situation, adding: "The safety and security of American citizens and US personnel overseas is our highest priority."

"The situation on the ground obviously could change quickly, and so we'll continue to evaluate and update our posture as needed," Ms Psaki added.

The assault on the Benghazi mission roiled the 2012 presidential campaign, and Republicans are still raising questions alleging the Obama administration was involved in a cover-up over who was behind the attack.