The order requires the Office of the National Intelligence Director to conduct regular assessments about potential foreign interference in the elections, asks for reports by the Homeland Security and Justice departments in the case of meddling in campaign-related infrastructure, he said.
Those sanctions could include blocking access to property and interests, restricting access to the US financial system, prohibiting investment in companies found to be involved, and even prohibiting individuals from entering the United States.
The executive order is being framed as an effort to demonstrate strength on the issue of election interference.
The move comes less than two months before the 2018 midterm elections, and just weeks after Dan Coats, Trump's director of national intelligence, warned of a "pervasive messaging campaign by Russian Federation to try to weaken and divide the United States" before Americans go to the polls in November.
Director of National Intelligence Dan Coats said this will be a 24-hour-a-day effort until election day.
But since becoming president, Trump has repeatedly dismissed the idea that he was helped by Moscow, calling it "fake news", and has avoided criticising Putin.
The White House has worked to push back against accusations that Trump was not seriously committed to aggressively protecting US elections from interference, especially after his press conference with Russian President Vladimir Putin in July.
"Today's announcement by the administration recognizes the threat, but does not go far enough to address it", Van Hollen and Rubio said.
"As I have made clear, the United States will not tolerate any form of foreign meddling in our elections".
In his first public comments since he retired in June, Rogers said: "That should concern us as citizens".
The president appeared to side with Mr. Putin and against US intelligence agencies that said the Kremlin meddled in 2016 to sow division, hurt Democrat Hillary Clinton and help Mr. Trump.
Bolton said the order was necessary to ensure a formal process and authorisation for sanctions, but he said he was in talks with lawmakers about legislation as well. Congress passed a Russian Federation sanctions bill more than a year ago.
"I don't know that it will be a complete solution", he said.
The order sets up a 90-day time frame for assessing reports of any kind of interference by foreign individuals and companies, and then deciding on the appropriate sanctions, which include freezing assets, banning business dealings with Americans and locking the actors out of the United States financial system.
"I think his actions speak for themselves", Bolton said.
"If we are going to actually deter Russian Federation and others from interfering in our elections in the future, we need to spell out strong, clear consequences, without ambiguity", Warner added.
USA lawmakers have introduced various pieces of Russia-related legislation, including the "Deter Act", to set out punishments for election meddling, and what one lawmaker called a sanctions bill "from hell" to punish Moscow for cyber crime and its activities in Syria, Ukraine and elsewhere.