"As I have made clear, the United States will not tolerate any form of foreign meddling in our elections".
"The executive order is not country-specific", Bolton said.
"If we see something, there's going to be an automatic response to that", Coats said.
At that same press conference, Trump blamed tensions between the United States and Russian Federation on special counsel Robert Mueller, whose investigation into Moscow's interference in the 2016 election is routinely slammed as a "witch hunt" by the president.
The order also is aimed at deterring the kind of election influence allegedly carried out by Russia in the 2016 presidential election, when USA intelligence services claim Russian entities spread disinformation in efforts to influence the balloting.
The 2018 US midterms are less than two months away and authorities are pre-empting foreign attacks on the elections based on USA intelligence.
"The president has acted decisively today", Bolton said, adding that the administration looked forward to engaging with Congress further on the issue.
That this announcement came first as a leak to USA news outlets and then as an announcement from National Security Advisor John Bolton underlines how fraught a subject it is for this particular White House.
The order comes two months before Americans go to the polls in elections that will determine control of Congress, potentially dramatically reshaping the balance of power in Washington.
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The lawmakers said Trump's executive order does not change the need for legislation.
The White House declined to comment.
'That It's something he cares deeply about that the integrity of our elections and our constitutional process are a high priority to him, ' Bolton said. "The United States can and must do more", such as the mandatory sanctions attached to legislation they proposed, the senators wrote.
According to the order, an array of federal agencies will be tapped to serve as the decision makers on whether interference has occurred.
Sen. Mark R. Warner, Virginia Republican and vice chairman of the Senate Select Committee on Intelligence, said the order gave too much discretion to the president.
While Trump has at times said he believes Moscow meddled, he has been quick to also point fingers of blame at China and individuals, including independent hackers.
"While the administration has yet to share the full text, an executive order that inevitably leaves the President broad discretion to decide whether to impose tough sanctions against those who attack our democracy is insufficient", said Sen Mark Warner, D-Va., the top Democrat on the Senate investigation into Russian Federation.
Sources told CBS News Tuesday the executive order does not mention Russian Federation by name. Congress passed a Russian Federation sanctions bill more than a year ago.
Trump has been dogged by accusations that he has not given enough credence to foreign interference in the U.S. election system, including in the 2016 race he won against Hillary Clinton. US, India sign deal on sharing intel Lawmakers introduce resolution to back naming North Atlantic Treaty Organisation headquarters after McCain Obama readies fall campaign push, but some Dems say no thanks MORE (D-Md.) introduced the Defending Elections from Threats by Establishing Redlines (DETER) Act earlier this year, which would penalize Russian Federation or other foreign governments that try to interfere in USA elections.