The President was advised that his tweeting only gives oxygen to the topic, even if those around Trump do not believe there is any truly new development, an informed source told CNN on Monday.
On Sunday, Trump tweeted an apparent response to stories by CNN and The Washington Post that said he was worried about his son Donald Trump Jr.'s legal exposure following the 2016 meeting.
Calling the reported concerns a "complete fabrication", the President acknowledged that the meeting was accepted on the premise that his son would get dirt on former presidential hopeful Hillary Clinton.
"This was a meeting to get information on an opponent, totally legal and done all the time in politics - and it went nowhere. I did not know about it!" the President tweeted.
The President's Sunday move about the purpose behind the 2016 Trump Tower meeting was the latest step in the long-evolving story from him, Donald Trump Jr. and the President's legal team.
Donald Trump Jr. initially responded to the first revelations about the meeting by releasing a misleading statement claiming the meeting primarily concerned Russian adoption policy.
As more details emerged, he released a new statement acknowledging there was an offer of potentially damaging information on Clinton and the Democratic Party, and he eventually published emails about the meeting.