They hand out soccer balls to children and halt traffic so elderly people can safely cross busy streets. They high-five bemused youngsters who follow them everywhere.

In Baghdad and throughout Iraq, the U.S. military is taking steps big and small to win over Iraqis, many of whom remain suspicious of American intentions. It's part of a carrot and stick policy (search) designed to root out insurgents who've been increasing attacks on Americans -- while at the same time assuring Iraqis that America means well.

On the surface, America's charm offensive seems to be doing well -- with children, teenagers and even some adults thrilled by the presence of the Americans, sometimes treating them like celebrities.

But the campaign is doing little to calm anti-U.S. sentiment and is highlighting the huge cultural gap between Iraqis and Americans -- a gap that some Iraqis believe no act of magnanimity or amount of cultural sensitivity can bridge.

From an Iraqi viewpoint, the two sides are oceans apart -- a conservative and proud people who are deeply conscious of their Arab and Muslim heritage and an occupying army that represents a faraway superpower seen in Iraq as arrogant, untrustworthy, an enemy of Islam and a friend of arch enemy Israel.

In Fallujah (search), a city west of Baghdad where resentment of the United States became intense after 18 people were shot dead by U.S. soldiers in April, American forces followed up on raids this week against suspected hideouts of hard-core Saddam Hussein (search) loyalists with goodwill gestures across the city of 200,000 people.

They handed out meals to school teachers who hadn't been paid, cleared fields for use as soccer fields, removed rotting garbage and gave teddy bears to children.

"This is American food. It isn't Iraqi," protested Abdel-Wahid Mansour, head of the Fallujah education district as soldiers unloaded 2,000 vegetarian meals for his teachers. "I don't deal with Americans and we don't need their food."

Every one of the female teachers at Fallujah's Martyr Abed Fazaa primary school for girls wears a scarf, a sign of Islamic piety. They all dismissed as unnecessary an American gift of blackboards and ceiling fans for the 634-pupil school.

Sensing their resentment of his American employers, an Iraqi male translator sought to reassure them. "God has sent these men from heaven to help us," he said. They remained unmoved.

In Baghdad, soldiers from the 82nd Airborne Division said they had been invited to "clean up" the area outside a mosque housing the tomb of Imam Mousa Kazim (search), a revered Shiite saint.

Soon after their arrival in mid-June, the bustling commercial area became the most intensive theater of spontaneous interaction between U.S. troops and ordinary Iraqis in Baghdad.

Constantly sweating in Baghdad's brutal summer heat, the men of the 82nd stopped traffic for old women to cross the street, ordered double-parking motorists to move on and endured, with surprisingly good humor, the swarms of children and teenagers who won't leave them alone.

They obliged passers-by who wanted to pose next to them for photographs and administered first aid to a boy with a cut on his hand. In a society that was notorious for its corruption under Saddam, they sought to demonstrate the notion of one law for everyone, admonishing a police officer in front of bemused onlookers for leaving his car in a no-parking zone.

"Sir," shouted one soldier, "As a police officer, you must set an example for everyone."

But no amount of good will could quell Abdel-Hameed al-Assadi's resentment of America.

"It is shocking," al-Assadi, a 56-year-old civil servant said about the American presence outside the mosque. Pausing before sunset prayers, he added: "To see Americans standing like this in front of the imam's shrine? My God, it's a bitter medicine that we must swallow."

After the Americans arrived, a large sign went up on the mosque's outside wall declaring: "This is a holy place just for Muslims." Pointedly, the sign is in English.

Lt. Daniel Akbar, a platoon commander from Athens, Ohio, has instructed his men to be culturally sensitive. Don't get too close to the mosque, avoid making eye contact with women and be polite to everyone are among the "rules of engagement" in the area.

"It's the first time that I have been around so many Iraqis," said Akbar, whose Middle Eastern looks have made him something of a sensation to the area's children. They tirelessly follow him around, taking turns at high-fiving him.

"We are not happy about the Americans being here," said Ahmed Hussein, a 24-year-old mosque guard. "But what can we do?" he said, as the air filled with the melancholic voice of a sheik reciting Quranic verses over the mosque's loudspeakers.

The atmosphere inside the mosque belied the tension outside it. Men, women and children venerated the Shiite saint, seeking his blessing by quietly touching the shrine's silver bars. On the white marble plaza surrounding the mosque, families squatted peacefully on blankets, as adults read from the Quran and small children played.

But the presence of Americans weighed heavily on the mind of Hussein Ali, a 40-year-old laborer and father of six.

"We'll force them to leave when the right time comes," he said. Then he fell silent and whispered: "How do we know that there are no Israelis among them?"