KABUL - Explosions and gunfire rang out as militants stormed the elite American University of Afghanistan in Kabul Wednesday, prompting desperate calls for help from students trapped inside classrooms, in the latest attack in the Afghan capital.

No group has so far claimed responsibility for the assault, which comes just weeks after two university professors - an American and an Australian - were kidnapped at gunpoint near the school.

Dozens of special forces cordoned off the area after the attack started on Wednesday evening, when the private university is usually packed with students, many of them working professionals doing part-time courses.

"I heard explosions and gunfire is going on close by... our classroom is filled with smoke and dust," said an anxious student.

"We are stuck inside and very afraid," she told AFP by telephone.

Many other trapped students were tweeting desperate messages for help, with some using classroom furniture to barricade the doors.

Among them was Associated Press photojournalist Massoud Hossaini, who was said to be wounded and later managed to escape with some fellow students.

"Many students have been evacuated," said interior ministry spokesman Sediq Sediqqi, adding that there were no immediate reports of any hostages taken by the attackers.

"We are not sure about the number of attackers... but our special forces have started clearance operations."

US military advisers were assisting Afghan forces to respond to the attack, an American defense official said. Kabul-based journalist Ahmad Mukhtar, a university student, tweeted that he managed to escape but "several of my friends and professors (are) trapped inside".

Ambulances rushed to the scene as erratic gunshots rang out from inside the campus.

The Italian-run Emergency Hospital in Kabul tweeted that at least five wounded people had been brought to the facility for treatment.

The attack, which underscores the worsening security situation in Afghanistan, comes as Taliban insurgents step up their summer fighting season against the Western-backed Kabul government.

The management of the American University of Afghanistan, which opened in 2006 and enrols more than 1,700 students, was not immediately reachable for comment.

The foreign professors at the university were seized from their vehicle on August 7, as the kidnappers smashed the passenger window and hauled them away at gunpoint.

It appeared to be the first reported abduction related to a private university in Afghanistan.

Their whereabouts are still unknown and no group so far has publicly claimed responsibility for the abductions, the latest in a series of kidnappings in the conflict-torn country.

The Afghan capital is infested with organised criminal gangs who stage kidnappings for ransom, often targeting foreigners and wealthy Afghans, and sometimes handing them over to insurgent groups.

The uptick in violence comes as the Taliban escalate nationwide attacks.

Afghan forces backed by US troops are seeking to head off a potential Taliban takeover of Lashkar Gah, the capital of the southern opium-rich province of Helmand as fighting intensifies.

The turmoil convulsing Helmand, blighted by a huge opium harvest that helps fund the insurgency, has left thousands of people displaced, sparking a humanitarian crisis as officials report food and water shortages.

The Taliban have also closed in on Kunduz -- the northern city they briefly seized last year in their biggest military victory so far -- leaving Afghan forces stretched on multiple fronts.

But coalition forces have insisted that neither Kunduz nor Lashkar Gah are at risk of falling to the insurgents.