By: the BBC
US media reports said he had shared material that was passed on by a partner that had not given permission.
The White House refused to comment on reports that Israel was the source.
Though not illegal, Mr Trump’s alleged gaffe is seen as a breach of trust by many in the intelligence community.
Mr Trump met Sergei Lavrov last week in the Oval Office, out of view of the US media.
Leading Republicans and Democrats have voiced concerns over what was said, with top Senate Democrat leader Chuck Schumer calling for the transcripts to be released by the White House.
The US Senate Intelligence Committee has also asked for copies of any notes taken in the meeting. CIA Director Mike Pompeo is due to brief the committee later.
Mr Trump’s alleged disclosures are not illegal, as the US president has the authority to declassify information.
What was the president’s defence?
Mr Trump tweeted: “As President I wanted to share with Russia (at an openly scheduled W.H. meeting) which I have the absolute right to do, facts pertaining to terrorism and airline flight safety.
“Humanitarian reasons, plus I want Russia to greatly step up their fight against [IS] & terrorism.”
It is not clear if Mr Trump was acknowledging having shared intelligence secrets with the Russian officials, thus contradicting White House statements, or whether he was simply trying to explain what had been discussed.