H R McMaster said instead the focus of the debate should now be on the "leaks" to the media and how "those violating confidentiality" have put America's national security at risk.
McMaster was present at the meeting when, according to a report in The Washington Post, Trump discussed "highly classified" details about the Islamic State terrorist group and laptops on plane with Russian Foreign Minister Sergei Lavrov and the country's ambassador Sergey Kislyak.
Citing current and former officials, it reported that the information shared by a US partner through an intelligence- sharing arrangement was so sensitive that it was withheld from allies and tightly restricted even within the US government. The officials said Trump's disclosures jeopardised a critical source of intelligence on the Islamic State.
But McMaster, at a crowded White House news conference, said Trump "wasn't even aware of where this information came from. He wasn't briefed on the sources or method."
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"I think the real issue and what I would like to see debated more is that our national security has been put at risk by those violating confidentiality. I think national security is put at risk by this leak and leaks like this," he said.
A day earlier, McMaster told reporters that the report was false. Today, he reiterated that claim.
"What I'm saying is really that the premise of that article is false, that in any way the president had a conversation that was inappropriate or that resulted in any kind of lapse in national security," he said.
"In the context of that discussion, what the president discussed with the (Russian) foreign minister was wholly appropriate to that conversation," McMaster said.
Democrats and some even from Trump's Republican party have questioned his wisdom in discussing matters of national security within the administration and outside.
Democratic leader Nancy Pelosi said in a statement that if the news reports are true, Trump has "compromised a key source of intelligence collection" against the Islamic State and jeopardised the security of the American people.