The New York Times reported on Saturday the president's eldest son met with the Russian lawyer. The story said she has possible connections to the Kremlin.
On Sunday, Trump Jr. acknowledged that he met with Veselnitskaya after he was told she might have information "helpful" to his father's presidential campaign.
On Monday night, the Times cited sources as saying that Trump Jr. was told in an email that he would receive compromising information on Hillary Clinton as part of a Russian government effort to aid his father's campaign. The 2016 email was reportedly aimed to set up the meeting with Veselnitskaya.
In the NBC interview, Veselnitskaya confirmed that Trump's son-in-law, Jared Kushner, and then-campaign manager Paul Manafort were also at the meeting. She said Kushner left after only seven to 10 minutes and Manafort never took part in the conversation, and instead looked at his phone.
"He was reading something. He never took an active part in the information," she said in Russian.
Veselnitskaya also described how the past few days have been since the story broke.
"You wake up one morning and you find you're the focus of all the high ranking, upstream media of the world," she said via a translator.
Veselnitskaya also claimed she was looking to meet with influential Americans about Russian adoption issues and was invited to meet with Trump Jr.
On Tuesday morning, Trump Jr. tweeted about the talks surrounding Russia.
—NBC News contributed to this report.
WATCH: Here's Donald Trump Jr.'s full statement on his meeting with a Russian lawyer