"We want elections for a democratic and united government," says Mohammed Al-Alewy, spokesperson for the group.
"It was unfair not to give us a place," in the interim Governing Council set up by the coalition in July, adds Essar Jafar, deputy secretary-general.
He would welcome the opportunity to prove his point in snap elections, for which top Shiite leader Abdul Aziz Al-Hakim, the current president of the Governing Council, and his Supreme Council of the Islamic Revolution in Iraq (SCIRI) has already called.
Jafar says his movement was formed in 1981 and boasts 150 000 militants and 176 offices all over Iraq, particularly in the Shiite south and in Baghdad.
Seven hundred Hezbollah militants were kiled by the regime of Saddam Hussein, he says in an interview.
He "supports those who filled the political void after the fall of Saddam Hussein," referring to members of the council, but bemoans the fact that many "did not make the same sacrifice".
"They are not popular, but they are closer to the coalition," he says.
The Hezbollah leaders have not really warmed to firebrand Shiite figure Moqtada Sadr, who strongly protests the US presence and finds support in the same poor Shiite quarters of the capital as Hezbollah.
"He has his opinions but we are not in conflict with him at the moment. He will get what he deserves, good or bad," says Jafar.
Alewy voices bitterness that Hezbollah can no longer go after the partisans of Saddam.
"His father, his mother and six brothers were killed by Saddam's men," notes Jafar.
"It is legitimate to hunt them, but the Americans stop us. When power is transferred we will be able to take action," he warns, adding however, "sadistic crimes" should be tried by courts.
The deputy secretary-general wants Hezbollah activists to be allowed to join the new police and army, and criticises the US for blocking it.
"If I have any advice to give them it's to use the know-how and knowledge of the terrain that Iraqis have and they lack. It's a major mistake to use former members of Saddam's security forces".
The Hezbollah today has a party headquarters, but ironically it is in the former prison where its members where once tortured and it is still largely a ruin.
Jawad Kazem al-Khirsan, a journalist with the Hezbollah weekly newspaper Al-Baina (Evidence), shows cell number 17 where he spent six months between November 2001 and April 2002.
"We want to turn it into a museum of Saddam's crimes," he says of the 90 cells on two floors.
Several Hezbollah cadres have been working among the debris, exposed wiring and broken pipes since May when they were allowed to move in without paying rent.
The state of the building appears to confirm that they do not receive any financial aid from abroad.
Inside, there are none of the portraits of Iran's revered late leader Ayatollah Ruhollah Khomeini nor globe and gun signs associated with the Lebanese Hezbollah.
"We have a strategy that is completely different and our movement was set up before" the Lebanese variety, notes Jafar, who wears western dress.
The fundamentalist Hezbollah in Lebanon, supported by Iran and Syria, emerged after the Israeli invasion in 1982.
It formed a spearhead in the fight against Israeli occupation of southern Lebanon. – Sapa-AFP.