Every night is a night of fear in the house of the date palms, a luxurious villa in the western suburbs of Tripoli. Its occupants are among thousands of city residents scared of being arrested by Islamist militias of Libya Dawn, which last week took over the Libyan capital and are targeting those from opposing tribes.

Like many of their neighbours, this family – at their request of anonymity – has sent the women away to safety, but the men left behind face a dilemma. If they leave too, the house, which has elegant carefully-tended date palms in the small courtyard, will likely be broken into and robbed. If they stay, and the militias find them, it could be worse.

"We can't leave, or the place will be destroyed," says the youngest son, a student. "We have to stay. These are long nights, I am telling you."

A particular feature of the occupation of Tripoli by Libya Dawn, the newest of the Middle East's self-proclaimed revolutionary movements, is the focus on residents from the wrong tribe.

The city was captured after a five week battle, involving heavy and indiscriminate artillery bombardments between Libya Dawn and tribal fighters from Zintan, Warshafan and Warfallah. Now residents whose family names indicate membership of those tribes are being rounded-up, whatever their politics, however tenuous their connection with those tribes.

"It happened to a neighbour in another street a few nights ago," says the student. "They stopped him at a stop light and saw his name. He was beaten and they took him in his own car to his house and broke [destroyed] it."

He is not the only one. Libya's Grand Mufti, Sheikh Sadik Al-Ghariani, its highest spiritual authority, broadcasting messages of support from a location in the UK, urged Libya Dawn to take a "firm hand" in their newly acquired city, and militias appear to have taken the message to heart.

By day, columns of smoke rise from houses of government supporters set alight, with the Libya Herald newspaper reporting 280 arson attacks, including on the villa of the caretaker prime minister, Abdullah Al-Thinni who has fled. By night, residents from pro-government tribes barricade themselves in their homes.

Attacks and looting have broken out across the city with the interior and electricity ministries and the prime minister's office ransacked. One woman tweeted returning home to the plush seafront district of Regatta to find it smashed and her property gone.

On Sunday , the US embassy residential compound, evacuated a month ago, also fell foul of the militias. A commander announced it had been "secured".

A Facebook group spent much of last week trying to find officials from the Red Crescent to retrieve ten unidentified bodies dumped at the interior ministry, stormed and abandoned by Misrata militias.

And militants have finally achieved their goal of attacking Tripoli's most noted landmark, the Gazella, a bronze fountain depicting a naked nymph and a gazelle bequeathed to the city by Italian occupiers in the 1930s.

A previous attempt by Islamists to destroy the statue, popularly known as the "naked lady", was halted by local residents forming a human chain around the site. But with the Libya Dawn takeover, an anti-tank rocket has blown a hole in the nymph.

"To hell with the statue, people are being attacked," said the student.

He is unable to sleep, waiting each night for a knock on the door, a vigil often by candlelight as the city suffers frequent power cuts.

Militias have also attacked a Tripoli refugee camp, Yarmouk, housing people from Tawargha, a town captured by Misrata militias during the 2011 uprising against Muammar Gaddafi. Five residents are reported to have been kidnapped, with tribal elders asking the authorities to hand them back. Reporters without Borders says journalists are also increasingly a target, with correspondents encouraged to report "good news" and several TV stations ransacked. Two producers from Al-Dawliya TV station were kidnapped.

"At first, they were just stopped and questioned at a checkpoint, but when it emerged that they worked for Al Dawliya, they were insulted and beaten, and then detained," said Reporters Without Borders. "They were finally freed after being mistreated and roughed up for five days."

Libya Dawn, an alliance of Islamists and militias from Misrata, 100 miles east, has broken with the newly elected parliament in Tobruk, setting up its own government, with a former Islamic fighter, Omar Al-Hasi, declared its "prime minister".

Its leaders, declared "terrorists" by parliament, insist they support democracy.

The Grand Mufti has called on Dawn units to refrain from looting, and Al Hasi says he supports law and order. "We reject extremism and terrorism. I am not with a specific group, party, operation or city but stand for a government for all Libyans."

But Tripoli's new rulers seem to lack the skills, or inclination, to administer their newly acquired city, with cuts to water, electricity and petrol common.

Anxious to shore-up support among a restive populace, Libya Dawn bused-in supporters from Misrata to hold a televised rally in the central Martyrs Square, a technique, opponents complained, which was last employed by Gaddafi.

Tripoli is these days a tale of two cities. While fear stalks the western suburbs, something approaching normality has returned to eastern districts, home to many Dawn supporters.

This new reality has caused bitter exchanges on social media, straining friendships. "Reminder: Those who claim things are great in Tripoli are most likely to be on Fajir (Dawn) Libya's side," wrote one tweeter. "It isn't great for those who had their homes burnt down or had to flee Fajir (Dawn) Libya's terror."

Fighting has spread along the coast towards the Tunisian border. In Benghazi, Islamist militia Ansar al Sharia, blamed by Washington for the killing its ambassador Chris Stevens in the city two years ago, is closing-in on the Benina airport. An overnight bombardment of the airport by grad rockets killed ten soldiers and wounded 25.

Western leaders have again called for a ceasefire, but diplomats say there is reluctance to answer Libya's pleas for military intervention, amid fears that the war will tip into a wider conflict between the United Arab Emirates, which support the nationalists, and Qatar, which backs the Islamists.