The defense filing was far shorter than the House managers’ memorandum, but White House lawyers have until noon on Monday to produce a more comprehensive legal brief laying out the case they will make on the floor of the Senate.

The House can then submit a written rebuttal by Tuesday. If all goes according to plan, the managers will begin live presentations in the Senate on Wednesday, and under an expedited schedule being contemplated by Senate Republicans, the president’s team could begin its presentation on Friday.

The defense filing on Saturday argued that Mr. Trump “has not in any way abused the powers of the presidency,” and that the July 25 call between Mr. Trump and the president of Ukraine was “perfectly legal, entirely appropriate, and taken in furtherance of our national interest.”

The arguments by Mr. Trump’s lawyers tracked closely with those presented throughout the House inquiry by Republicans in that chamber, like Representative Jim Jordan of Ohio and Mark Meadows of North Carolina, who did not dispute what had occurred so much as the idea that the president had been acting on some corrupt scheme.

The document appeared intended to appeal to Mr. Trump’s sensibilities. It accused Mr. Schiff of “creating a fraudulent version” of the July 25 call when he jokingly offered a hypothetical conversation during a congressional hearing, something that Mr. Trump has repeatedly mocked Mr. Schiff for doing.

As they have said for weeks, the president’s lawyers asserted that the articles of impeachment against Mr. Trump are “invalid on their face” because they do not accuse the president of breaking any law.

But the Democrats argued in their memorandum that impeachable actions “need not be indictable offenses,” a theory that has been espoused by many legal scholars. The framers of the Constitution, they argued, intended the remedy for “acts committed by public officials that inflict severe harm on the constitutional order.”