President George Bush has said he "sympathised" with the mother of a US soldier killed in Iraq but refused to heed her call to pull out the troops.
Sheehan refuses to leave until she gets an audience with the president
Speaking from his Texas ranch where Cindy Sheehan has been holding a roadside protest, Mr Bush said withdrawing would be a "mistake".
Ms Sheehan is vowing to remain until she gets to speak to the president about his justification for the war.
Dozens of well-wishers have turned out to join her demonstration.
"Listen, I sympathize with Mrs Sheehan," Mr Bush said. "She feels strongly about her position.
"And she has every right in the world to say what she believes. This is America."
He said he had thought "long and hard about her position" calling for US troops to be sent home.
But he had decided against it, he said.
"It would be a mistake for the security of this country and the ability to lay the foundations for peace in the long run if we were to do so," he said.
Mr Bush's remarks came after meeting with security advisors, including Vice-President Dick Cheney, Defence Secretary Donald Rumsfeld and Secretary of State Condoleezza Rice.
Ms Sheehan's son Casey was killed in Baghdad's Sadr City in April 2004.
The Californian has been camped outside Mr Bush's property since Saturday and has become a symbol for the US anti-war movement.
"All I want is for President Bush to take one hour out of his vacation and meet with me before another mother's son dies in Iraq," she said.
"You don't use our country's precious sons and daughters unless it's absolutely necessary to defend America."
However, some veterans and relatives have dubbed the vigil a distraction and are keen to ensure support for those serving in Iraq does not wane.
Ms Sheehan met the president once before when he visited Fort Lewis in Washington state to meet relatives of those killed in the war.