US President Donald Trump ordered senior staff after they joined the White House to sign non-disclosure agreements following several leaks in the early months of his administration, according to The Washington Post.

The agreements stipulated officials could face monetary penalties if they disclosed confidential White House information to the press or others, and were intended to remain in effect after Trump was no longer president, according to the report published Sunday.

A draft copy of the agreement would have subjected violators to a $10 million penalty for each instance, payable to the US Treasury, according to Ruth Marcus, the Post's deputy editorial page editor. Sources familiar with the final document do not remember a similarly large penalty, she said.

Top officials in the Trump campaign signed similar agreements, but legal experts questioned whether such an agreement would be legal for a high-ranking government employee, given constitutional free-speech protections.

Officials ultimately agreed to sign the agreements, in part after concluding they were likely not enforceable, according to the Post.

The White House did not immediately respond to a request for comment.