House Intelligence Committee Chairman Adam Schiff (D-CA) speaks during a news conference about impeachment proceedings at the U.S. Capitol in Washington, September 25, 2019.

The chairman of one of the Democratic-led U.S. House of Representatives committees leading the impeachment probe of President Donald Trump said on Friday the committee would continue and "accelerate" its efforts.

"We expect to announce additional testimony from relevant witnesses in the coming days and remain prepared to compel testimony through duly authorized subpoenas as appropriate," Representative Adam Schiff, chairman of the House Intelligence Committee, said in a letter to fellow House members on Friday.

"We have anticipated from the outset of this investigation that the White House would fall back on political attacks or nonsensical legal arguments to distract from the President's misconduct," Schiff added.

So far, House Democrats have subpoenaed a swath of government agencies and individuals as part of the impeachment inquiry. Those individuals include Secretary of Energy Rick Perry and two associates of President Trump's personal lawyer Rudy Giuliani, Igor Fruman and Lev Parnas, who were arrested Thursday on campaign finance violations. The White House, Office of Management and Budget, Department of Defense, and State Department have all been subpoenaed as well.

The White House, however, said on Tuesday it would refuse to comply with requests from House Democrats.

Schiff's letter confirmed that the House scheduled depositions with a former Senior Director of the National Security Council Dr. Fiona Hill, who oversaw European and Russian affairs and left her post in August. Other future testimonies include those from State Department Deputy Assistant Secretary George Kent, State Department Counselor T. Ulrich Brechbul, and E.U. Ambassador Gordon Sondland.

Earlier Friday, the U.S. ambassador to Ukraine Marie Yovanovitch testified to House impeachment investigators that President Trump personally pressured the State Department to oust her.

CNBC's Ganesh Setty contributed to this report.