LONDON, Feb 10 (Reuters) - U.S. Treasury yields traded steadily on Monday, shrugging off remarks over the weekend from President Donald Trump that his administration could look into Treasury debt payments for evidence of possible fraud.

Trump, who was speaking to reporters aboard Air Force One on Sunday, suggested that the country's $36 trillion debt load might not be that high.

"We're even looking at Treasuries," he said. "There could be a problem - you've been reading about that, with Treasuries and that could be an interesting problem."

He added: "It could be that a lot of those things don't count. In other words, that some of that stuff that we're finding is very fraudulent, therefore maybe we have less debt than we thought."

The yield on the benchmark 10-year Treasury note US10YT=RR showed little reaction, edging up 1.2 basis points on the day to just below 4.50%, while two-year yields US2YT=RR were flat at 4.28%.

It was not clear whether Trump was referring to debt service or other government payments made by the Treasury Department.

Neither the White House nor the Treasury Department were immediately available for comment when contacted by Reuters.

"It is virtually impossible that President Trump’s comments refer to the debt held by the public, including foreign holders. This is the reason the market is not reacting and any reaction would be based on misunderstandings or misinformation,” said Maria Vassalou, head of the Pictet Research Institute.

She noted that around a fifth of gross U.S. federal debt is held in government accounts, mostly related to social security retirement funds and healthcare programmes, and Trump's comments "most likely refer to that portion of U.S. debt".

“(Markets) do care and should care, absolutely, given the $35 odd trillion in public debt," Martin Whetton, head of financial markets strategy at Westpac in Sydney, said.

"In short, until it is clarified it is meaningless.”

With little in the way of clarity over what Trump may have meant, the focus in markets remained on the economy and what the Federal Reserve might do with interest rates in the coming months, after having left them unchanged at the January meeting.

Friday's U.S. nonfarm payrolls report showed an increase of 143,000 workers in January, compared with expectations for a rise of 170,000, while December's number was revised up to 307,000.

The data perked up the dollar, but did little to change expectations for monetary policy.

The futures market shows traders currently believe the Fed will cut rates at least once this year, with a roughly-50/50 possibility of a second quarter-point reduction.

(Reporting by Amanda Cooper in London and Rae Wee and Tom Westbrook in Singapore; editing by Mark Heinrich)

((amanda.cooper@thomsonreuters.com; +442031978531; Bluesky: @acoops.bsky.social;))