Cipollone wrote that Trump's lawyers "cannot fairly be expected to participate in a hearing while the witnesses are yet to be named and while it remains unclear whether the Judiciary Committee will afford the president a fair process through additional hearings."
The counsel also said Trump would be in London for the NATO leaders meeting on Wednesday.
The hearing is the Judiciary Committee's first. It is due to look at the legal basis for the investigation of the president and will feature legal scholars.
"An invitation to an academic discussion with law professors does not begin to provide the president with any semblance of a fair process," Cipollone said in the letter.
The letter was in response to a request by Nadler for Trump to indicate by Sunday whether the president himself or his attorneys would attend Wednesday's hearing.
Cipollone wrote that the White House would respond separately regarding participation in future hearings by Friday, a further deadline set by Nadler.
The inquiry enters a crucial week as the House Intelligence Committee plans to vote on a report making the case for Trump's removal from office on Tuesday. Their findings would go to the Judiciary Committee to consider actual charges.
The impeachment inquiry began in September, as Democrats alleged the Republican president abused the power of his office by pushing Ukraine to investigate his rival, Joe Biden.
The saga also hinges on whether Trump withheld military aid to Ukraine as part of the pressure campaign.
Public hearings began in November.
The Trump administration has been stonewalling the impeachment inquiry as much as possible. The president maintains he has done nothing wrong.
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