Kennedy, a leading member of the opposition Democratic Party, also likened the situation in Iraq to the 1954-1962 Algerian war for independence from France.
"Iraq could very well be another Algeria, where the French won the military battle for Algiers, but ultimately lost the political battle for Algeria," Kennedy said in an address at Johns Hopkins University in Washington.
Iraq's elections are taking place Sunday.
"Once the elections are behind us and the democratic transition is under way, President (George W.) Bush should immediately announce his intention to negotiate a timetable for a drawdown of American combat forces with the new Iraqi government," the veteran senator said.
"At least 12,000 American troops and probably more should leave at once, to send a stronger signal about our intentions and to ease the pervasive sense of occupation," Kennedy added, suggesting: "America's goal should be to complete our military withdrawal as early as possible in 2006."
"The men and women of our armed forces are serving honorably and with great courage under extreme conditions, but their indefinite presence is fanning the flames of conflict," Kennedy warned.
Republican National Committee communications chief Brian Jones countered that "it's remarkable that Senator Kennedy would deliver such an overtly pessimistic message only days before the Iraqi election."
"Kennedy's partisan political attack stands in stark contrast to President Bush's vision of spreading freedom around the world," Jones added. "The world is watching whether America has the will to stand with the Iraqi people as freedom takes root in their nation, and no democracy has ever risen out of defeatism."