Bush supporters gathered for an event marking the culmination of the "You don't speak for me, Cindy!" tour, which started last week in California. The crowd of about 1,500 chanted, "Cindy, go home!"
"You are giving hope and encouragement to the enemies of America," said former California Assemblyman Howard Kaloogian, a Republican who co-founded the group that coordinated the rally.
Meanwhile, busloads of war protesters gathered several miles away at "Camp Casey," named for Sheehan's 24-year-old son who died in Iraq last year.
CBS News Correspondent Mark Knoller reports that President Bush remained on the grounds of his ranch behind a security perimeter but he made his case about Iraq in his Saturday radio address.
"Our efforts in Iraq and the broader Middle East will require more time, more sacrifice and continued resolve," Mr. Bush said. "Yet people across the Middle East are choosing a future of freedom and prosperity and hope."
A bell-ringing ceremony on Saturday honored soldiers serving in Iraq. Organizers estimated the crowd at more than 2,000 but it appeared smaller.
"I know that the Camp Casey movement is going to end the war in Iraq," Sheehan said, adding that no other families should have to suffer the loss of a relative. She led the crowd in chanting "Not one more!"
At the pro-Bush rally several miles away, there were some heated moments when two members of Protest Warrior, a group that frequently holds counter protests to anti-war rallies, walked in with a sign that read "Say No to War — Unless a Democrat is President."
Many Bush supporters only saw the top of the sign and believed the men were war protesters, so they began shouting and chasing the pair out. One man tore up their signs. When Will Marean of Minneapolis, Minnesota, kept repeating that he was on the Bush side and tried to explain Protest Warrior's mission, one Bush supporter shook his hand and apologized.
A few Bush supporters went to the edge of the anti-war camp on Saturday, trying to remove some of the hundreds of white crosses bearing fallen soldiers' names. They had a list from families who did not want their sons' or daughters' names associated with Sheehan's group.
Sheriff's deputies said they could remove the name tags but not the crosses, so the group removed a few tags and left without incident.
Sheehan, of Vacaville, California, started camping out off the road leading to Bush's ranch on Aug. 6, soon after the president's Texas vacation began. She vowed to remain unless he talked to her about the war with Iraq that claimed the life of her son Casey and more than 1,870 other U.S. soldiers.
Sheehan said that after the protest ends Wednesday, some of the group will spread its message on a tour, with the first stop probably in the Texas district of Republican Tom DeLay, the Majority Leader of the U.S. House of Representatives.
Bush has said he appreciates Sheehan's right to protest and understands her anguish but will not change his schedule to meet with her. His vacation is to end Sept. 2.
Sheehan and other grieving families met with Bush about two months after her son died last year, before she became a vocal opponent of the war.