President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE indicated Thursday the White House would seek to limit testimony from former national security adviser John Bolton John BoltonDiplomacy with China is good for America The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep DOJ launches probe into Bolton book for possible classified information disclosures MORE if he were called to testify in a Senate impeachment trial.

Trump reiterated that he would defer to the Senate on whether Bolton would be allowed to testify, but made clear the White House may seek to claim executive privilege to limit what he could say.

"I'd have to ask the lawyers because we do have to — to me, for the future — we have to protect presidential privilege," he continued. "When we start allowing national security advisers to just go up and say whatever they want to say, we can’t do that."

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"So we have to protect presidential privilege. For me, but for future presidents," he added. "People can’t go up and say whatever my thoughts are, whatever your thoughts are about us, countries' views. You don't want that to be out."

The White House blocked several witnesses from testifying during the House impeachment inquiry last year.

Bolton said in a statement Monday that he would be willing to testify in a Senate impeachment trial if subpoenaed, even over administration objections.

Bolton's testimony would be a boon to Democrats seeking to build a case against Trump in the looming Senate impeachment trial. The former national security adviser, who left his post in September, was mentioned repeatedly during House testimony late last year.

It remains unclear whether any witnesses will be called, however, as GOP senators appear to be in agreement on beginning the trial without a commitment to hearing from witnesses.

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The House impeached Trump in December for abuse of power and obstruction of Congress after alleging he made security aid and a White House meeting for Ukraine contingent on the country announcing investigations into his political rivals.

Bolton described the effort by administration officials to press Ukraine for the investigations as a “drug deal,” according to witness testimony in the House impeachment inquiry. His attorneys have also said he has relevant information on meetings and conversations regarding Ukraine.

Trump, who has repeatedly called the impeachment proceedings a "hoax" and denied wrongdoing, said Thursday he would like to see former Vice President Joe Biden Joe BidenCast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response Biden tells CNN town hall that he has benefited from white privilege MORE, his son Hunter Biden and House Intelligence Committee Chairman Adam Schiff Adam Bennett SchiffOvernight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Overnight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings MORE (D-Calif.) testify in a Senate trial.

But the White House has increasingly dialed back its desire to hear from witnesses in favor of a quick trial that ends in Trump's acquittal.

The timing of the trial remains unclear as the House has yet to submit the articles of impeachment to the upper chamber. Speaker Nancy Pelosi Nancy PelosiMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Pelosi must go — the House is in dire need of new leadership MORE (D-Calif.) told reporters Thursday that she would do so "soon."