The soldiers said they did not think it was worth their while to be in Iraq and questioned the use of repeated tours of duty.
The campaign, called the Appeal for Redress from the War in Iraq, takes advantage of defence department rules allowing active duty troops to express personal opinions to politicians without fear of retaliation.
The appeal posted on the campaign's website at www.appealforredress.org said: "As a patriotic American proud to serve the nation in uniform, I respectfully urge my political leaders in congress to support the prompt withdrawal of all American military forces and bases from Iraq.
"Staying in Iraq will not work and is not worth the price. It is time for US troops to come home."
The website allows service members to sign the appeal that will be presented to members of congress. Organisers said the number of signatories had climbed from 65 to 219 since the appeal was posted a few days ago and Wednesday when it was publicly launched.
There are 140,000 US troops in Iraq.
Military service personnel on active duty are restricted in expressing their personal views, but rules in the Military Whistleblower Protection Act give them the right to speak to a member of congress while off duty and out of uniform, while making it clear that they do not speak for the military.
In a conference call with reporters, a sailor, a marine and a soldier who had served in the Iraq operation said American troops there have increasingly had difficulty seeing the purpose of lengthy and repeated tours of duty since the fall of Saddam Hussein.
"Staying in Iraq will not work and is not worth the price. It is time for US troops to come home"
Appeal for Redress from the War in Iraq website
Their misgivings have intensified this year, they said.
"The real grievances are: Why are we in Iraq if the weapons of mass destruction are not found, if the links to al-Qaeda are not substantiated," Marine Sergeant Liam Madden, who was in Iraq from September 2004 to February 2005, said.
Navy Seaman Jonathan Hutto, the first serviceman to join the campaign, said a similar appeal during the Vietnam war drew support from more than 250,000 active duty service members in the early 1970s.