Virginia Sen. Mark Warner, in an interview on CNN's "State of the Union," said that he had been briefed earlier Sunday morning and investigators were still unsure if the attacks were "inspired" or "directed" by militants abroad, like ISIS or al Qaeda.
"There is no specific threat against the United States," Warner added.
On Saturday, masked men wearing fake suicide belts used a van to mow down pedestrians
on London Bridge before stabbing people in the nearby Borough Market area.
The attack came about two weeks after a concert bombing
in the northern UK city of Manchester.
Asked why the US has not seen the same kind of repeated incidents the UK has in recent weeks, Warner said he believed the US has better integrated immigrants into society, including Muslim-Americans. But Warner said President Donald Trump could be going against that trend in his response to the attacks.
"That's why it troubles me so much to see the type of tweets the President has put out in the last twelve hours or so," Warner said.
Trump reacted to the attack on Twitter, saying the US would do anything it could to help the UK and that people "must stop being politically correct."
He also took a shot at London Mayor Sadiq Khan, writing, "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'"
In the wake of Saturday evening's attacks, Khan called the attackers
"cowardly terrorists" and said London was safe.
"Londoners will see an increased police presence today and over the course of the next few days -- no reason to be alarmed," Khan said.