Tester said he expects a resolution to this investigation in the first or second week following that.
"Admiral Jackson has been on the front lines of deadly combat and saved the lives of many others in service to this country", White House spokesman Hogan Gidley said in a statement.
He spoke to reporters before meeting Tuesday afternoon with Republican Sen. Patty Murray, D-Wash., a member of the Veterans' Affairs Committee.
In video captured by MSNBC, Jackson says he looks forward to "answering everybody's questions" when the hearing is rescheduled.
Jackson had denied the existence of any such report just hours earlier.
The White House Medical Unit in 2012 - led by current Veterans Affairs nominee Ronny Jackson - was described by one staffer as the "worst command ever".
At the time of the report, Kuhlman was the physician to the president.
According to the report, Jackson admitted he had failed to shield the White House medical unit from the leadership drama.
Jackson is quoted saying he was willing to do what was necessary to straighten out the command, even if it "meant finding a new position in Navy Medicine".
In addition to Jackson's lack of management experience at a large organization, the physician had come under fire for his glowing appraisal of Trump's health after the president had his annual physical in January.
A 2012 watchdog report ordered up by Veterans Affairs nominee Dr. Ronny Jackson found that both he and a rival physician exhibited "unprofessional behaviors" as they engaged in a power struggle over the White House medical unit.
Trump's appointment of Jackson continues the president's pattern of rewarding loyalty instead of merit, a move that seems to be fueled by his own sense of personal political survival. The report initially was reviewed by The Associated Press. The document described the working environment as akin to "being caught between parents going through a bitter divorce".
The allegations about Jackson add to worries from senators in both parties that Jackson is not qualified to run the veterans agency. "It's totally his decision", the president said, blaming Democratic obstruction and scrutiny.
Armenia: calls for new rally after talks on replacing prime minister halted
People celebrate Armenian prime minister Serzh Sarkisian's resignation in downtown Yerevan, April 23, 2018. It was not immediately clear whether that signalled specific support for Pashinyan's candidacy or not.
Trump is criticizing members of Congress who questioned Jackson's lack of experience.
Trump called Jackson "one of the finest people that I have met". Johnny Isakson, R-Ga., the chairman of the panel.
We take very seriously our constitutional duty to thoroughly and carefully vet each nominee sent to the Senate for confirmation.
"We're gonna have a hearing at some time in the future, but not Wednesday", said Sen.
The statement and the letter to the president didn't detail what new information was brought to their attention about Jackson, a rear admiral who has served in the White House under three presidents. It seeks any communication between the Pentagon and the White House regarding "allegations or incidents" involving him.
Senate Veterans Affairs Committee members are assessing allegations from whistleblowers that have told the panel about Jackson's questionable behavior including excessive drinking and a "toxic" work environment under his leadership, according to two former White House medical staff members who have spoken with the committee.
Spokeswoman Amanda Maddox cites questions from lawmakers over allegations made about Jackson's past behavior.
But now the Senate has indefinitely delayed the doctor's confirmation hearing, scheduled for today, and the prognosis is not good.
The Senate has increasingly become a partisan battleground for nomination fights, a war that escalated when President Barack Obama was in the White House and Senate Democrats, who had majority control, changed the rules to allow majority vote for confirming most nominees - the so-called nuclear option - to get around GOP filibusters.
The former colleagues said he was nicknamed "Candyman" because of how freely he distributed medications, a moniker Tester told CNN that he heard about as well from Jackson's associates.
But White House physicians, including Jackson's predecessors, have for years distributed small amounts of Ambien, a prescription sleep aid, to White House staff and members of the press flying on long overseas trips.
Isakson, a Georgia Republican, declined to say anything more at the Capitol.