Washington (CNN) Attempted Russian interference in US public affairs has continued as Department of Homeland Security officials and senior leaders have alerted the White House about the risks ahead of the 2020 presidential election -- but it was "like pulling teeth" to get the White House to pay attention, a US government official told CNN Wednesday.

One reason for the difficulty, according to the official, is that "in general, senior White House staff felt it wasn't a good idea to bring up issues related to Russia in front of the President."

Officials have "spent months and months trying to sound alarm at the White House about the need to take foreign interference more seriously and elevate the issue," the official said, adding that Director of National Intelligence Dan Coats shared those views and feels the administration "was not being forward-leaning enough in notifying Congress and the American people."

The official noted that there have been one or two principals' meetings before the midterm elections, as well as a press conference in which national security adviser John Bolton, then-Homeland Security Secretary Kirstjen Nielsen, FBI Director Christopher Wray and National Security Agency Director Paul Nakasone warned the public of election interference.

The government official said DHS and other agencies made repeated requests to set up more Cabinet-level meetings on the subject and Bolton's National Security Council rebuffed the requests.

"They (DHS) kept 'getting the Heisman' from Bolton and company," the official said.

The bigger concern, the official said, was post-2018 midterms and the need to sit down and figure out how to coordinate a better whole-of-government response, "to get everyone out of their silos. But it was like pulling teeth to get the White House to focus the attention needed on this."

Garrett Marquis, a spokesman for the NSC, told CNN that "any suggestion that this administration is giving less than a full-throated effort to secure America's elections is patently false."

The Department of Homeland Security declined to comment.

In a statement to CNN, Coats said the idea that the Trump administration doesn't take election security seriously is inaccurate.

"The implication by anonymous sources that the Administration has not or is not taking this issue seriously is false and minimizes the work that continues to be advanced by countless individuals to ensure the integrity of our electoral process," Coats said. "Moreover, these claims may undermine the public's confidence in our work, thereby supporting our adversaries' agenda."

He added that the White House was always open to him briefing Trump on election security.

"I know, because I specifically asked the President for certain capabilities on behalf of the Intelligence Community and he quickly agreed and also encouraged several of us to speak to the American people," Coats said. "That support has not changed and the inter-agency continues to work tirelessly to prepare for the 2020 elections. Election security is and will continue to be one of our nation's highest national security priorities."

Raises concerns over future readiness

The lack of urgency by the White House and the desire to keep the issue away from Trump -- which was first reported by The New York Times -- raises fresh questions about the readiness of US defenses against foreign interference in the next presidential election. On Tuesday, White House senior adviser Jared Kushner downplayed Russian meddling efforts and suggested that US investigations into them were more harmful than the foreign interference.

Last week, special counsel Robert Mueller said in a redacted version of his report on Russian interference in the 2016 election that a Russian troll group engaged in a years-long campaign to sow discord in the US -- and eventually to support Trump's election -- by creating and maintaining fake social media personas and activist organizations designed to look like they were run by real Americans.

Citing interviews with three unnamed senior administration officials and one former senior official, the Times said Nielsen, who left the White House earlier this month, was told by acting White House chief of staff Mick Mulvaney in a meeting this year that Trump "still equated any public discussion of malign Russian election activity with questions about the legitimacy of his victory."

In a statement to CNN regarding the Times' report, Mulvaney said he didn't "recall anything along those lines happening in any meeting" and insisted that the Trump administration has done more to combat Russian meddling than Barack Obama's administration.

"In fact, for the first time in history, state, local, and federal governments have coordinated in all 50 states to share intelligence, we've broadened our efforts to combat meddling by engaging the Department of Homeland Security, the Department of Justice and the FBI among others, and we have even conducted security breach training drills to ensure preparedness," Mulvaney said.

Nielsen's role

Two administration officials offered conflicting views about Nielsen's determination to make election security a priority for the Trump administration.

A senior administration official tells CNN that while Nielsen grew frustrated with the White House's lack of engagement on election security, she continued to push the matter on her own, organizing two principals' meetings on her own -- hosted at DHS offices in the Washington, DC, area.

Nielsen also pressed to brief members of Congress on election threats and the administration's defense efforts, participating in briefings for the House and Senate on election security, this official said. Her efforts, and those of DHS and other agencies, also took place outside of DC, participating in an election security summit in St. Louis, meeting with secretaries of state at conventions to talk about DHS support, and was involved in a tabletop "election apocalypse" exercise in Colorado.

"Nielsen pushed the idea that election security is national security," the senior administration official said. "There's a set of facts here that reflects how seriously she and DHS took this."

The official said there was a "real frustration" from administration officials who wanted a "more strategic approach" rather than written policy declarations.

"Ultimately, it would have been a good thing for the President to make a strong public statement on the security efforts around the 2018 election, but it wasn't going to happen," the official said.

A senior White House official, however, pushed back against the Times' report about Nielsen's efforts to raise the issue, suggesting that the former DHS secretary was trying to improve her image with the public.

"Someone is trying to do a rehabilitation tour," the official said. "She wants to be seen in a positive light."

The official believes Nielsen was trying to broaden her legacy by the end of her tenure and "didn't want to be thought of as the Secretary of Immigration."

Still, the official conceded Trump and the West Wing staff were more focused on border security than on cybersecurity at the time, saying the border was "sucking up all the oxygen in the room."

The official also insisted the White House is determined to stop Russia from interfering in the 2020 election.

"These aren't topics we shy away from," said the official, who added that there was a sense in the West Wing that the DHS proposals for dealing with the Russia threat were not "fully baked" enough to warrant a meeting with the President.