In the memo, Defense Secretary Jim Mattis said that the DoD did have some concern that recommendations could negatively impact allies, but that it agreed with the Department of Commerce's conclusion that imports of foreign steel and aluminum based on unfair trading practices were a threat to national security
Earlier this month, the Commerce Department recommended imposing heavy tariffs or quotas on foreign producers of steel and aluminum in the interest of national security, following a trade investigation of imports.
"DoD continues to be concerned about the negative impact on our key allies regarding the recommended options in the report," he said.
However, Mattis said that among the alternatives, targeted tariffs are "more preferable than a global quota or global tariff."
"In addition, we recommend an inter-agency group further refine the targeted tariffs, so as to creative incentives for trade partners to work with the U.S. on addressing the underlying issue of Chinese transshipment," Mattis said, in the memo.
He stressed: "It is critical that we reinforce to our key allies that these actions are focused on correcting Chinese overproduction and countering their attempts to circumvent existing anti-dumping tariffs — not the bilateral U.S. relationship."
If President Donald Trump decides to move forward with targeted tariffs or quotas on steel, Mattis recommended that the labor leaders and management of the impacted industries be convened by the president so they would understand that the tariffs and quotas are conditional.
If the administration takes action on steel, the DoD recommends waiting before taking any further steps on aluminum, he said.
"The prospect of trade action on aluminum may be sufficient to coerce improved behavior of bad actors ... it remains important for the President to continue to communicate the negative consequences of unfair trade practices," Mattis said.
Trump and his administration announced the so-called Section 232 investigation into steel and aluminum imports in April. The investigation sought to determine whether the imports posed a threat to national security.
On Feb. 16, Ross reported that steel is in fact important to U.S. national security, and current import flows are adversely impacting the steel industry.
"[T]he Secretary of Commerce concludes that the present quantities and circumstance of steel imports are 'weakening our internal economy' and threaten to impair the national security as defined in Section 232," the department said.
— CNBC's Kayla Tausche and Tom DiChristopher contributed to this report.