President Trump’s attorneys sent their written counteroffer Wednesday to special counsel Robert Mueller on a potential interview of the president, reportedly rejecting Mr. Mueller’s proposed terms and urging him to wrap up his probe quickly.

“We have responded in writing to the latest proposal from the Office of Special Counsel regarding its request to interview the president,” said attorney Jay Sekulow. “It is not appropriate at this time to comment publicly about the content of that response.”

The Washington Post, citing people familiar with the matter, said Mr. Trump’s lawyers rejected the special counsel’s latest terms for an interview in the Russia investigation, instead offering a narrow path for answering questions. They reportedly said they consider questioning the president about possible obstruction of justice to be legally inappropriate.

“Millions of pages of documents, along with testimony from dozens of witnesses, have been provided. We are restating what we have been saying for months. It is time for the Office of Special Counsel to conclude its inquiry without further delay,” Trump lawyer Rudolph W. Giuliani said in a statement.

He said he wants the investigation to be wrapped up by Sept. 1.

Wednesday’s letter to Mr. Mueller is expected to be the last word from the president’s legal team on the terms of a possible interview.

Earlier, Mr. Giuliani told CNN that the letter would represent “a good-faith attempt to reach an agreement” with the special counsel’s office on any interview between Mr. Mueller and the president. He said questions about Mr. Trump’s comments on former national security adviser Michael Flynn and fired FBI Director James Comey would be off-limits because the president’s legal team considers those subjects “perjury traps.”

“For example: ‘What did you say about Flynn?’ ‘Why did you fire Comey?’” They already know our answer,” Mr. Giuliani said.

Mr. Giuliani said the president’s legal team would not give Mr. Mueller “a straight turndown” of his request to interview the president.

The two sides have been negotiating for eight months over an interview of the president.

Last week, Mr. Mueller sent a proposal to Mr. Trump’s legal team, laying out topics for questioning the president: Russia’s interference in the 2016 presidential election and if any of Mr. Trump’s campaign associates colluded with the Russians, and whether the president tried to obstruct the probe.

The investigators agreed to accept some answers in writing from the president, with the possibility of follow-up questions in person.

Mr. Trump periodically has expressed an interest in sitting down with investigators to answer questions. But he also has repeatedly criticized Mr. Mueller’s investigation as a partisan “witch hunt” and the claims of Russian collusion as a Democrat-inspired “hoax.” Allies of the president have worried aloud that his freewheeling style of conversation could get him into legal trouble in a formal interview with prosecutors.