Story Highlights• Sen. John McCain says media failing to report improving security conditions
• Congressman: Lawmakers encouraged to remove helmets during Baghdad tour
• Military investigating how explosives-laden suicide vests ended up in Green Zone
• Roadside bombs in Salaheddin province kill four, wound eight
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BAGHDAD, Iraq (CNN) -- Sen. John McCain visited a Baghdad market Sunday and later told reporters the American people were not getting the full story on what he said were improving security conditions in the war-ravaged capital.
McCain, a presidential hopeful, was among a delegation of Republican lawmakers that made an unannounced trip to Iraq this weekend, the details of which were withheld for security reasons.
Accompanied by a military escort, the delegation traveled in armored Humvees to Baghdad's main marketplace, which has seen numerous attacks in recent months, including a grenade attack in March.
After going to Shorja market -- where a triple car bombing in February killed 79 people and wounded 170 -- McCain told reporters at a Green Zone news conference that the recent surge of U.S. troops gives the military "a very good chance of bringing security." (Watch how Congress and the White House are tussling over a deadline to bring troops home )
"The American people are not getting the full picture of what's happening here. They are not getting the full picture of the drop in murders, the establishment of security outposts throughout the city, the situation in Anbar, the deployment of additional Iraqi brigades who are performing well and other signs of progress," he said.
McCain has said he backs President Bush's plan to deploy 25,000 troops to Baghdad and Anbar province in an effort to fight terrorism and sectarian violence in the regions.
While some of the troops have been deployed, the entire force will not hit the ground for four more months, White House counselor Dan Bartlett said Sunday on ABC's "This Week."
In his Sunday remarks, McCain conceded that Baghdad is still dangerous, but said he believes the U.S. military has "a new strategy that is making progress."
The Arizona Republican, who is one of the war's most outspoken supporters, became testy when pressed about his recent remarks that there are areas of Baghdad where Americans can travel safely.
"I just came from one," he said, referring to his trip to the outdoor market, which required a heavy military escort. "I've been here many times over the years. Never have I been able to drive from the airport. Never have I been able to go out into the city as I was today."
McCain further emphasized that his previous remarks did not mean the fight to secure Baghdad was over, but rather, that "things are better and there are encouraging signs."
The senator was joined on the trip by Sen. Lindsey Graham of South Carolina and Reps. Rick Renzi of Arizona and Mike Pence of Indiana.
Graham, who was on his sixth trip to Iraq, said his past visits have required more security than Sunday's trip.
Gen. David Petraeus, the top U.S. commander there, was so confident in the security situation that he told the lawmakers they could remove their helmets "at our discretion," Pence said. They retained their body armor, he said.
"We moved and mingled among some of the warmest and most welcoming people that I've ever met on the face of the earth," Pence added.
Explosive vests found in Green Zone
U.S. military investigators are trying to determine how two explosives-laden suicide vests made it past security and into the heavily fortified Green Zone.
The vests had not been detonated when they were discovered Saturday, and military spokesman Rear Adm. Mark Fox said the find was indicative of "the nature of the security challenge that we're facing."
"Even in areas where there's extreme high levels of security, there are times where we have to be very careful and very scrutinizing of the kinds of security measures that we exercise," he said.
Attackers have hammered the Green Zone in recent days. A U.S. soldier and American contractor were killed and five people were wounded when a rocket landed in the cordoned-off area Tuesday.
The 4-square-mile area, aka the International Zone, is the location of the Iraqi parliament and government offices.
The Pentagon has required all personnel to wear body armor and helmets when outside buildings in the Green Zone, a source there said.
Bombs rock Salaheddin
Roadside bombs in Salaheddin province, north of Baghdad, killed four people and wounded eight others Sunday, a Tikrit police official said.
The deadliest attack targeted an outdoor market in Tuz Khurmatu, a mixed Shiite and Sunni Kurd town about 100 miles (170 kilometers) north of Baghdad, killing three people and wounding seven.
Two hours later, another attack on an Iraqi police patrol in Dhuluiya, about 50 miles (85 kilometers) north of Baghdad, killed one police officer and wounded another.
Dhuluiya is where Iraqi security forces last month arrested the local leader of the insurgent group, Islamic State of Iraq. Five of his aides also were arrested, security sources said. The group is believed to be linked to al Qaeda.
CNN's Mohammed Tawfeeq and Candy Crowley contributed to this report.
Sen. John McCain speaks to reporters Sunday in the Green Zone during an unannounced visit to Iraq.