"One aviation source said that there are suicide bombers who have entered an area where there are fuel tanks and a substantial amount of fuel so the situation is still on going."
Bays said at least three suicide attackers were involved in the incident.
Barack Obama, the US president, has ordered 30,000 more troops into Afghanistan, in part to back up a planned offensive in Kandahar, the biggest operation of the nearly nine-year-old war.
However, the Taliban has launched increasingly deadly attacks in advance of the offensive, with at least 20 civilians being killed since April 12.
Our correspondent said the Taliban has pledged to fight very strongly against the US offensive, which is expected to begin in June.
"Some on the ground believe the Taliban have actually launched their own offensive ahead of the Nato assault," he said.
"Al Jazeera is learning from Taliban sources that now there are Taliban units roaming the city and they have been given authority to carry out independent operations without going through their headquarters.
"When they see an opportunity to strike, they'll do it."
The attack came shortly after the United Nations announced it had temporarily shut its office in Kandahar due to security concerns.
Al Jazeera has learned that the UN made the move on Tuesday in response to a specific threat issued by the Taliban, although a UN spokesman said it was because of a deteriorating security situation.
The UN has now pulled back its international staff from Kandahar to Kabul, and has told its Afghan employees to stay at home for the next few days.
Our correspondent said the UN reduced the number of its international staff in Kandahar after learning of the threat from a local religious leader.
"...The Taliban went to the local cleric [at a local mosque near the UN headquarters in the city] and told him to warn residents living around the UN headquarters that they should leave their homes because there was about to be an attack on the UN."
The UN maintained about 40 international staff in Kandahar about a year ago. Now the number is fewer than 10, all of whom have currently been withdrawn.
Our correspondent said the withdrawal of the UN staff is under review. But he said that their return to the office is unlikely until after the planned Nato offensive.
However, Ahmad Wali Karzai, a senior government official in Kandahar province and the half brother of Hamid Karzai, the Afghan president, played down the threat to the UN and said the UN was overreacting by withdrawing its staff.
Ahmad Karzai said that the security situation in Kandahar was far worse a few years ago, and he urged the international aid community not to scale back operations in the city.
"We strongly condemn this act by the UN to pull out of Kandahar," he said.
"This is an irrational decision [done] without consulting with local authorities."
By contrast, Khalid Pashtoon, an Afghan member of parliament, told Al Jazeera: "In Kandahar the situation has been deteriorating for the last few weeks due to the forthcoming Nato operation.
"The Taliban is starting a new strategy. They are concentrating more in the city of Kandahar, terrorising tribal elders or government officials.
"For the last two or three few weeks, more than a dozen important people have been terrorised in Kandahar."
Pashtoon said that the Nato offensive must go ahead, although there have been concerns that support must first be secured with local tribal leaders.
"If they don't conduct the operation, the situation will become even worse because this will be like a defeat to the interntional community."