Several blasts were heard after the warplane started circling above the battered city on Tuesday evening.
Earlier, the interim Iraqi government issued an ultimatum that was seen as the latest in a series of threats by the US-backed government to the al-Mahdi Army.
The al-Mahdi Army is loyal to Shia leader Muqtada al-Sadr and has been fighting US occupation soldiers around the Imam Ali mosque for the past three weeks.
"We are in the last hours. This evening, Iraqi forces will reach the doors of the shrine and control it and appeal to the al-Mahdi Army to throw down their weapons," Defence Minister Hazim al-Shaalan told a news conference at a US military base outside Najaf.
"If they do not, we will wipe them out."
A spokesman for al-Sadr's office in Baghdad, Raid al-Kadhimy, said: "This is the beginning of the battle."
To the death
"They [US forces] will not enter Najaf until we are all dead," al-Kadhimy told Aljazeera.
He also said "those collaborators with the US forces will be sooner or later heavily punished by the Iraqi people and al-Sadr's movement".
"The whole world has witnessed al-Sadr welcoming any peaceful initiative," al-Kadhimy continued.
"We still welcome any peaceful initiative"
al-Sadr spokesman in Baghdad
"But those crooked members of the government, who are collaborating with the US occupation forces, do not want any peace. They are slaves for the occupation forces.
"However, we still welcome any peaceful initiative," al-Kadhimy added.
He stressed that al-Sadr was willing to hand over the shrine's keys to Ayat Allah al-Sistani and evacuate al-Haidari compound.
"But those [government members] are manipulating us... They are not cooperating with us to hand over the keys, which is considered the beginning of a peaceful solution for our crisis.
"Even Saddam Hussein has not dared to attack the holy shrines," al-Kadhimy added.
Meanwhile, US tanks on Tuesday reinforced their positions along the southern flank of the shrine.
Witnesses near the shrine said they saw Iraqi forces for the first time in the battle zone, after a morning of intense gunfire following fierce attacks by US warplanes overnight.
US tanks have reinforced their
positions near the shrine
"I saw at least 10 American tanks parked on Medina street. It was impossible to get through today because snipers were everywhere," said one Iraqi witness, Fadil Shakir.
Medina street is a strategic thoroughfare with snipers on both sides. It is about 500 metres from the shrine.
A witness reported seeing Iraqi National Guard troops in two white pickup trucks appear for the first time in the battle zone. Witnesses said they saw many of them as well as some policemen around Medina street.
The US military said a rocket fired by militiamen clipped the wall of the Imam Ali shrine on Tuesday and might have damaged the building.
In a statement, the military said US aircraft spotted militiamen firing the rocket from the northeast corner of Iraq's holiest Shia shrine.
"The rocket clipped the wall of the shrine and landed approximately 10 metres north of the wall. The shrine may have sustained damage due to the rocket," it said.
Each side in the Najaf fighting has accused the other of mounting attacks near the shrine and of failing to respect holy ground.