Chuck Schumer, a Democratic senator, said: "What this report makes crystal clear is that the cost to our country in lives lost and dollars spent is tragically unacceptable.
"The backbreaking costs of this war to American families, the federal budget and the entire economy are beyond measure in many ways."
Kimberly Halkett, Al Jazeera's Washington correspondent, said: "The report says the wars have so far cost the average American family nearly $21,000.
"The Democrats say that by 2017 that price will rise, costing a family more than $46,000."
The report's $3.5 trillion figure is $1.1 trillion higher than a non-partisan estimate by the congressional budget office last month.
The cost of the conflict in Iraq alone accounts for $1.3 trillion of the $3.5 figure, according to the report.
"We simply cannot buy victory in Iraq," Harry Reid, the Senate Democratic majority leader, said.
The White House has rejected the JEC report.
"This committee is known for being partisan and political. They did not consult or co-operate with the Republicans on the committee," Dana Perino, White House press secretary, said.
She called the report a "partisan attempt to overshadow positive developments in Iraq".
Jack Burkman, a Republican strategist, argues the figure released in Tuesday's report is deceptively high.
He said: "Our military, much more so than others throughout the world, is outsourced, so if you want to talk money and finance, it's just not as bad as people think."
The JEC estimate assumes the number of US troops in Iraq will reduce over time but a large-scale US force will be retained there.
The committee also estimated the cost of repair and refitting military equipment, the money needed to keep soldiers in the ranks and the costs to the US domestic economy of deploying US army reserve units.
The house of representatives will vote this week on another effort by Democrats to set a deadline for the withdrawal of troops from Iraq, making it a condition for providing another $50bn for the war.
The proposal would require the withdrawal or re-deployment of most troops in Iraq to begin immediately, with a goal of ending combat operations within a year.
George Bush, the US president, has repeatedly resisted attempts to force him to accept timelines for pulling troops out of Iraq.
If Bush vetoes the bill, "then the president won't get his $50bn", Reid said.