Washington (CNN) Republicans and Democrats are demanding more information about connections between President Donald Trump's former national security adviser Michael Flynn and several foreign entities -- including the Kremlin-backed media outlet RT.

Their calls come after months of controversy surrounding one of Trump's longtime campaign advisers and top aide on security matters. Questions have swirled about the nature of his ties to Russia and whether he violated any restrictions on contacts with foreign officials.

The top Democrat and Republican on the House Oversight Committee sent individual letters to four top Trump administration officials requesting any documents they have related to Flynn's communications with and payments from Russian, Turkish or other foreign sources.

"We are asking the Department of Defense and FBI and others to give us anything he has had to do with the Russian government and with Russians and others because he lied to us over and over again," Rep. Elijah Cummings of Maryland told CNN's "New Day" Thursday.

In the incident that led to his ouster from the National Security Council, Flynn acknowledged misleading Vice President Mike Pence about the nature of his communications with the Russian ambassador in Washington.

In addition, last week CNN reported that Cummings had obtained emails showing Flynn was paid more than $33,750 by Russia's state-run broadcaster RT TV-Russia for a speech in Moscow in December 2015, and received travel compensation from other Russian companies.

Flynn had previously acknowledged the speaking engagement, telling multiple news outlets in July and August that he received money for the speech. But he declined to state the amount and he told the media that the source of the funds was his US speakers bureau, not the Russian broadcaster.

Earlier this month, Cummings questioned whether Flynn had reported the payment as required by both law and military regulations. In addition, receiving money from a foreign government without approval from his relevant branch of service violates military regulations.

"We want to know what the President knew when he appointed him as security adviser," Cummings added.

Flynn had no comment regarding the committee's letters, according to spokesman Price Floyd.

Specifically, Cummings and committee chairman Jason Chaffetz of Utah have asked that each agency produce documents relating to Flynn's foreign contacts and payments, security clearance applications and other related documents between the time of his retirement in 2014 to today.

The committee has requested that all documents be provided by April 3.

The Oversight Committee's push for more information on Flynn comes just days after FBI Director James Comey told the House Intelligence Committee that the bureau is investigating the relationship between Trump's advisers and Russia to see if those ties played a role in Moscow's efforts to interfere with the 2016 US election.

During the hearing, Comey was asked for details related to the actions of several individuals who are either currently members of the Trump administration or were tied to his campaign team, including Flynn. Comey declined to answer questions relating to specific individuals, citing the ongoing investigation.

Flynn has previously denied improper contacts and CNN has not confirmed that he is among the subjects of the FBI's review.

Details linking Flynn to various foreign sources first emerged when Trump tapped him to be national security adviser in November 2016, but criticism of the former military man escalated earlier this year amidst controversy over his contacts with Russian Ambassador to the US Sergey Kislyak.

Flynn's resignation came in February after reports that the Trump administration was warned that he had misled administration officials regarding his communications with the Russian ambassador and was potentially vulnerable to blackmail by the Russians, a person familiar with the matter told CNN last month.

The concern was raised after Flynn claimed to administration officials that he had not discussed the Obama administration's recent sanctions on Moscow with the Russian ambassador. It is illegal for unauthorized private citizens to negotiate with foreign governments on behalf of the US.

Following initial reports in early January that Flynn was in contact with Kislyak and spoke to him about US sanctions, Vice President Mike Pence offered a robust defense of the incoming national security adviser. He said in nationally televised interviews that he had spoken with Flynn and that Flynn had ensured him he had not spoken about sanctions with the Russian ambassador.

The Justice Department, however, communicated to the White House that Flynn had misled administration officials.

Flynn wrote in his resignation letter that he had "inadvertently" briefed Pence and others in the White House with incomplete information about his contacts with Kislyak.

FBI officials told CNN last month that they do not plan to pursue charges against Flynn barring any new information, after he told agents he did not remember discussing sanctions with Kislyak.

However, reports of Flynn's dealings abroad have continued to appear even after his resignation.

Earlier this month, CNN reported that Flynn's consulting firm, FlynnIntel Group, received $530,000 in payments from a Turkish-owned company based in the Netherlands and registered as a foreign agent, or an entity that does lobbying work on behalf of a foreign government, with the Justice Department. He acknowledged that the work may have benefited the Turkish government, according to foreign agent registration paperwork filed with the Justice Department.

The work came at the height of the US presidential campaign while Flynn served as Trump's top foreign policy adviser on the campaign. The contract did not end until November 15, a week after Trump was elected president.

On March 10, the White House acknowledged that Trump's transition team was aware that Flynn engaged in work that would likely require him to register his consulting firm as a foreign agent before Flynn was picked to serve as national security adviser.

Less than a week later, on March 16, CNN reported on emails detailing Flynn's relationship with RT. The US intelligence community has long assessed RT to be a propaganda tool of the Kremlin, writing in its January report on Russian interference in the US election that the organization had participated in disinformation campaigns aimed at the US.

The letters from the Oversight Committee ask White House Chief of Staff Reince Priebus, FBI Director James Comey, Department of Defense Secretary James Mattis and Director of National Intelligence Daniel Coats to provide any documents related to Flynn in their possession.