Mowaffaq al-Rubaie told a televised news conference in Baghdad on Thursday that his country's security forces had seized documents giving them the edge over the group.
"We believe this is the beginning of the end of al-Qaeda in Iraq," he said.
Al-Rubaie had told Reuters earlier this year that those fighting the US-backed and predominantly Shia government had been defeated. But the violence has continued.
The Pentagon said on Thursday that 2,500 of its military personnel in Iraq had been killed since the invasion in 2003 and 18,490 wounded.
Tens of thousands of Iraqis have died.
However, al-Rubaie said on Thursday: "The government is on the attack now ... to destroy al-Qaeda and to finish this terrorist organisation in Iraq."
He said security forces have benefited from information found after Abu Musab al-Zarqawi, the erstwhile leader of al-Qaeda in Iraq, was killed by US action last week.
Holding out a piece of paper, al-Rubaie said: "I present to you a document that was found in one of Zarqawi's computers that reveals many dangerous things and gives details on strategy and plans of the al Qaeda terrorist organisation in Iraq."
But a copy of the document, the authenticity of which could not be independently verified, did not identify the anonymous author as an al-Qaeda member or give specific information about any planned attacks.
"I present to you a document that was found in one of Zarqawi's computers that reveals many dangerous things"
Instead, it suggested that fighters were being weakened by US raids and propaganda, and proposed ways to counter this - for example by infiltrating Iraq's armed forces, recruiting new members and making more weapons.
It also said the best way to get out of "the crisis" was to foster conflict between the US and another country, such as Iran, and by stirring US-Shia tension in Iraq.
Al-Rubaie said the material showed that al-Qaeda's strategy was to "divide, destroy and rule".
He said: "These documents have given us the edge over al-Qaeda and also gave us the whereabouts of their network, of their leaders, of their weapons and the way they lead the organisation and the whereabouts of their meetings."
"These documents have given us the edge over al-Qaeda"
But al-Qaeda in Iraq has vowed to fight on under its new leader, Abu Hamza al-Muhajir.
The US military said on Thursday it believed that his real name was Abu Ayyub al-Masri. They said he was an Egyptian, had trained in Afghanistan and formed al-Qaeda's first cell in Baghdad.
Also on Thursday, four people were killed and up to 20 wounded in a gun and grenade attack on a mosque near Tikrit, the home town of Saddam Hussein 175km north of Baghdad, witnesses said.
A nephew of one of those killed, citing witnesses, said seven masked gunmen in Arab dress opened fire as people left the mosque after morning prayers, killing one.
'People are very angry'
He said the attackers threw hand grenades as the people fled back inside, followed them and killed three others, including his uncle, Dawud al-Khalid.
"It is the first such incident in Alam," Muhammad al-Khalid said. "People are very angry."
Ten men were shot in Baquba
In Diyala province, north of Baghdad, 10 labourers were shot dead on their way to work in Baquba, the provincial capital. Police said gunmen stopped their minibus, ordered them out and killed them.