The call comes following reports that Mr Bolton made claims in an unpublished book that Mr Trump wanted to freeze aid to Ukraine unless it investigated his political rival, Democrat Joe Biden.
It could undermine Mr Trump’s defence.
The impeachment trial will resume in the US Senate later on Monday.
Mr Trump told reporters last week that he did not want Mr Bolton to testify.
The president is alleged to have withheld military aid to pressure Ukrainian President Volodymyr Zelensky into starting a corruption investigation into Mr Biden, and his son Hunter.
President Trump has repeatedly branded the impeachment proceedings a “witch hunt”.
What do the new reports allege?
On Sunday, the New York Times cited excerpts from an unpublished book by Mr Bolton.
They included claims that Mr Trump told a then-top aide in August that he wanted to withhold $391 million security aid to Ukraine until officials there assisted with probes into Democrats, including Mr Biden.
If true, such a claim would undermine the main argument of Mr Trump’s defence team that there was no “quid pro quo” which offered aid in return for investigating Mr Biden.
“Bolton directly contradicts the heart of the President’s defence,” House impeachment manager Adam Schiff tweeted.
“If the trial is to be fair, Senators must insist that Mr Bolton be called as a witness, and provide his notes and other documents.”
House Speaker Nancy Pelosi said that Republicans’ refusal to call Mr Bolton and others is “now even more indefensible”.
There has been no comment from Mr Bolton’s lawyers, nor from the White House.
The president has previously said he does not want Mr Bolton to testify on the grounds of national security.
The latest reports come after a video made public on Saturday showed Mr Trump ordering the removal of the US ambassador to Ukraine in 2018.
With Republicans holding a 53-47 majority in the Senate, it is unlikely that the president will be removed from office.