Amid reports of new attacks this week, which have killed dozens, al-Ja'fari said one area of success was a decrease in the frequency of car bombs. Before the formation of his government, he said, there were 12 to 14 such bombs per day and now there are only a few.
"Some days, it is two car bombs, some other times nothing," he said. "There has been a marked reduction. The same thing can be said of the other provinces. Hence, good progress has been made. People are going out. They used to go back home in the early evening hours, deserting the streets and public parks. Now Iraqis freely stroll out late in the evening. This is the difference from what we had before. To us there has been tangible progress in terms of security. We think that, God permitting, in the upward security trend as regards quantity, quality, and supplies, we will achieve sufficient capability for the multinational forces to leave Iraqi territory. The presence of multinational forces in a country is not a sign of strength."
Al-Ja'fari meets Bush on 24 June to discuss the status of security efforts, a crucial part of which is the training of Iraqi forces.
Al-Ja'fari also cited as progress on 23 June the recent agreement in which representatives of Iraq's Sunni Arab minority will serve on a Shi'a-dominated committee drafting the country's constitution. He said he will push the committee to complete the draft by the mid-August deadline.
He told the Council on Foreign Relations, a foreign-policy institute, the document would reflect Iraq's population, which is majority Muslim, but that it would not discriminate against minorities.
"This is a fact. Constitutions should respect their respective people. When there is a community in a country espousing a certain religion, this religion has to be respected as respect for the human being," al-Ja'fari said. "This is a man's right but a right that by no means allows him to encroach on the others. Democracy allows, nay, wants constitutions to accommodate the majority's right, but democracy does not allow the majority to deny the right of minorities and other groups. I am a strong believer in this truth."
U.S. lawmakers are worried by the slow progress so far in writing the constitution, saying delays feed the insurgency.
On 23 June, U.S. Defense Secretary Donald Rumsfeld and his top military advisers on Iraq faced seven hours of questioning by two U.S. Congressional panels.
The top Democrat on the U.S. Senate's Armed Services Committee, Carl Levin (Democrat-Michigan), told Rumsfeld the administration needs to apply more pressure on Iraqi officials to stick to their timetable for adopting a constitution. He said such pressure should include the threat of a pullout.
"We have opened the door for the Iraqis at great cost but only they can walk through it," Levin said during the hearing. "We cannot hold that door open indefinitely. Only a constitutional agreement, a political settlement, can change the status quo and end the insurgency in Iraq. The possibility of our leaving unless such a settlement is reached can help bring about that agreement."
The questions from Republican and Democratic lawmakers reflected domestic concerns about the intensity of the insurgency in the mostly Sunni Muslim areas of Iraq and the U.S. strategy there.
Some lawmakers are calling for the Bush administration to develop a timeline for withdrawal. But Rumsfeld said that would have a disastrous effect and serve to boost the insurgency.
In response to questioning from senators, Rumsfeld also said it was unwise for the United States to send in more troops to secure Iraq's borders from insurgents.
"You'd become a world class occupying power," he told lawmakers. "You would immediately assume all the burdens of the intrusiveness of hundreds of hundreds of hundreds of thousands of troops trying to seal that border."
But General George Casey, commander of multinational forces in Iraq, noted that more troops were brought in before the January parliamentary elections. He said his planners are looking ahead to October -- when Iraq holds a popular referendum on the constitution -- and if they reach a similar assessment, more troops will be sought.
The United States presently has almost 140,000 troops in Iraq. The Defense Department says Iraqi security forces who have received some training and equipment now number 168,500, including police and military personnel.
Public opinion polls show Bush is facing declining support from Americans for the Iraq campaign. Bush is to deliver what is being called a major speech on Iraq on 30 June. That is the first anniversary of the handover of power from the U.S.-led coalition to Iraqi authorities.