The committee said in a statement that it had issued subpoenas to former national security adviser Michael Flynn and one company associated with the former intelligence official, Flynn Intel Group LLC; and longtime Trump lawyer Michael Cohen and his firm, Michael D. Cohen & Associates PC.
Meanwhile, Trump and Russian President Vladimir Putin sounded similar tones as they criticized the ongoing US scrutiny of Russia's attempts to sway the presidential election.
Flynn has sought immunity in order to testify before any of the Russian Federation probes, and he initially cited his Fifth Amendment protection from incriminating himself when he first declined to hand over documents to Senate investigators.
Separately, Boris Epshteyn, a Trump campaign surrogate who briefly served in the White House press office, said in a statement that he also received a request from the House committee seeking information, a development first reported by CBS News.
Yesterday, Flynn agreed to turn over documents to the Senate Intelligence Committee concerning their investigation into Russia's activities during the 2016 campaign.
In an interview with French daily Le Figaro on Tuesday, Russian President Vladimir Putin described the allegations of Russian interference as "fiction" invented by Democrats to justify their election defeat.
But Cohen passed. He said the request was "poorly phrased, overly broad and not capable of being answered".
Explosion in diplomatic area of Kabul kills, wounds dozens
The U.S Embassy and the North Atlantic Treaty Organisation mission in Kabul are also near, about a half-mile away from the site. The most prominent terrorist group in the country, the Afghan Taliban , has denied any involvement and condemned the attack.
"If the reports are accurate, subpoenas related to the "unmasking" issue would have been sent by Chairman Nunes acting separately from the committee's Russian Federation investigation", the aide said in an email, referring to Rep. Devin Nunes, R-Calif., who recused himself from the Russian Federation probe after the House Ethics Committee said it was investigating him for improperly revealing classified information. Those committees are investigating any potential collusion between members of the Trump campaign and Russian agents during the election.
In May, the committee took testimony from former Central Intelligence Agency director Brennan, who said that he had become concerned during the election campaign by the contacts between Trump associates and the Russians and shared the information with the Federal Bureau of Investigation. News also confirmed the report. The Russian government denied any knowledge of such a plan.
Mr Cohen's business associates in the taxi enterprise included a number of men from the former Soviet Union, including his Ukrainian-born father-in-law.
The chairman and vice chairman of the committee, Sen.
Mr Cohen has made his own unsuccessful attempts at public office, losing a city council race and briefly running for state assembly in NY.
UPDATE: Fox News' James Rosen reports that Samantha Power, former U.S. Ambassador to the United Nations, and former CIA Director John Brennan were given subpoenas as well.