The letter from the federal safety agency outlines the problem saying: "The performance defect is that the fuel tanks installed on these vehicles are subject to failure when the vehicles are struck from the rear. Such failure can result in fuel leakage, which in the presence of external ignition sources, can result in fire. The design defect is the placement of the fuel tanks in the position behind the axle and how they were positioned, including their height above the roadway."
The NHTSA does not specify what remedy it believes Chrysler should pursue to fix the problem it alleges.
Chrysler has until June 18 to issue a formal response explaining why it will not comply with the recall request.
(Read More: Pickups Power May Auto Sales)
In a written statement, Chrysler CEO Sergio Marchionne defended the safety of the Jeep models in question saying: "The safety of drivers and passengers has long been the first priority for Chrysler brands and that commitment remains steadfast. The company stands behind the quality of its vehicles. All of us remain committed to continue working with NHTSA to provide information confirming the safety of these vehicles."
The 2.7 million Jeeps met federal vehicle safety standards when they were manufactured. The NHTSA agrees with this claim in its letter to Chrysler, but doesn't think that is enough. "The existence of a minimum standard does not require NHTSA to ignore deadly problems."
In a statement late Tuesday, NHTSA Administrator David Strickland said the agency's data show "these vehicles may contain a defect that presents an unreasonable risk to safety" and it "hopes that Chrysler will reconsider its position and take action to protect its customers and the driving public."
So why is Chrysler challenging the recall?
A source familiar with the situation, who asked to remain anonymous, says the automaker believes the rate of fatal rear-impact crashes for the Jeeps is no greater than the fatality rate for other vehicles involved in rear-impact crashes that result in a fire.
At issue is how to measure fatality rates for vehicles.
When taking a look at the number of fatal rear-impact crashes per millions of miles driven, the Jeep rate, according to sources, is lower. In addition, without a formal remedy suggested, the question becomes how would Chrysler ensure the safety of the Jeeps.
It's rare when a vehicle manufacturer balks at a NHTSA request for a recall.
(Read More: Leasing Hits New Highs, Auto Loans Surge)
Every year, there are dozens of recalls and most of the time the federal government, automakers and parts suppliers hold numerous discussions about the specific problem and how to fix it.
As one industry veteran described it, there's a healthy and vigorous debate, but eventually everyone involved agrees to a solution.
That's what makes Chrysler's response to the recall request so unusual. It is challenging the evidence, including pictures of many horrific fatal accidents, collected by the NHTSA.
Eventually, Chrysler and the NHTSA are likely to negotiate some type of settlement. If not, the matter could play out in a public hearing and be decided in court.
_ By CNBC's Phil LeBeau. Follow him on Twitter @LeBeauCarNews
Questions? Comments? BehindTheWheel@cnbc.com