 -- The top Democrat on the House Oversight Committee is raising questions about White House counselor Kellyanne Conway's air travel, and asking for proof that former Health and Human Services Secretary Tom Price has paid for his seats on controversial private flights.

In a letter to Conway obtained by ABC News, Rep. Elijah Cummings, D-Maryland, has asked Conway for information on all private, non-commercial and military flights she has taken.

Conway, who is the first White House official to be questioned regarding air travel, is coming under scrutiny after Price resigned Friday, and after reporting from Politico revealed that she joined Price on several chartered flights for events across the country.

“Despite the fact that you joined Secretary Price on several of these flights, you have not made any similar public statements indicating whether your own actions were appropriate, whether you will continue to take such flights at taxpayer expense in the future, or whether you plan to personally repay the taxpayers for the cost of your seats on these flights,” Cummings wrote.

A White House official told ABC News in response to questions about Conway's travel: "Agencies are responsible for arranging appropriate transportation for their own events. Members of the President’s Cabinet occasionally invite relevant White House staff for official travel for events promoting the President’s agenda. When White House staff are invited, their travel plans are planned and secured by the inviting agency."

In addition to Price, Interior Secretary Ryan Zinke, Veterans Affairs Secretary David Shulkin and Treasury Secretary Steven Mnuchin have all come under fire for their use of government planes or private aircraft.

The White House is taking steps to crack down on travel and use of private charters in the administration instead of commercial air travel. John Kelly, the White House chief of staff, will now sign off on all government and chartered air travel by agency leaders, according to a memo released by White House budget director Mick Mulvaney Friday.

“Every penny we spend comes from the taxpayer. We thus owe it to the taxpayer to work as hard managing that money wisely as the taxpayer must do to earn it in the first place,” he wrote.

On Friday, Price said in a statement that he plans to write a personal check to the Treasury for the expense of his travel.

According to a person familiar with the former secretary’s travel, Price’s seats on all the flights cost $51,877.31. But Price’s total travel has cost the government an estimated $400,000 in chartered aircraft expenses, according to Politico.

ABC News has reached out repeatedly to the Treasury Department and HHS asking if Price has actually written the promised check. A Treasury Department spokesman declined to reveal that information, citing privacy concerns, while HHS has declined to comment.

On Wednesday Cummings also sent a letter to Mnuchin and acting HHS Secretary Don Wright asking for proof of Price's pledge: a copy of his check reimbursing the government.

ABC's Justin Fishel and Katherine Faulders contributed to this report.