Mr. Trump’s step — which President Barack Obama had flirted with in 2013, but eventually did not undertake — was unprecedented. While treaties ban the use of chemical weapons, they do not authorize signatories to attack other countries for violating them. Moreover, in 2017, the United States acted without a multilateral alliance like NATO. (France and Britain participated in the April 2018 strikes.)

Eventually, after being sued under the Freedom of Information Act by a government watchdog group, Protect Democracy, the Trump administration disclosed that its legal team did draft and internally circulate a seven-page, unsigned memo analyzing a legal basis for potential military action against Syria. While the memo is undated, Justice Department lawyers said it was probably produced on April 6, 2017, the day of the first strikes.

But the administration has continued to keep the contents of that memo a secret. As a result, its completion and disclosure of the new memo, explaining why the Office of Legal Counsel blessed the April 2018 strikes, amounts to its most comprehensive discussion of its understanding of the scope of Mr. Trump’s war powers.

Still, Mr. Engel’s memo was solely devoted to the domestic law question of whether Mr. Trump could order such strikes without congressional permission. He did not acknowledge or address the separate international law question of whether the strike put the United States in breach of the United Nations Charter, a treaty it has ratified that permits one country to attack another only in self-defense or with Security Council authorization, and if so, why Mr. Trump could do that.

As a matter of domestic constitutional law, the scope of a president’s power to order limited attacks without congressional authorization is murky. Although the Constitution says Congress, not the president, has the power to declare war, many presidents of both parties have used force abroad without congressional authorization. Mr. Engel’s memo cited many such historical episodes and earlier memos as precedent.

For example, his formulation that presidents can unilaterally deploy troops into military operations whose limited nature, scope and duration mean they fall short of “war” in the constitutional sense, so long as doing so is in the national interest, was articulated in memos written during the Clinton administration by Walter Dellinger, who then ran the Office of Legal Counsel, in the context of interventions in Haiti and Bosnia.

Martin Lederman, a Georgetown law professor who worked in the Office of Legal Counsel in the Obama administration, praised Mr. Engel for emphasizing assessments that the airstrikes were unlikely to escalate into a broader conflict. Still, he noted a “tension” in the memo: Mr. Engel also cited as a precedent President Harry S. Truman’s decision to go into the Korean War — a major conflict — without congressional authorization.