Currently, foreign branches of U.S. institutions are not subject to the same rules as those in America.
The White House said that financial regulators are already working on ensuring the certainty that the bill's authors seek. As such, "passage of this bill would be premature and disruptive to the current and ongoing implementation of the reforms," it said.
It added, "The Administration believes regulators should be given the time necessary to complete their work."
The bill was approved by the Financial Services Committee on Monday and now heads to the full House.
Garrett is the chairman of the Financial Services subcommittee that oversees capital markets.
Reps. John Carney (D-Del.), Mike Conaway (R-Texas) and David Scott (D-Ga.) are cosponsors of the legislation.
--This story was updated at 6:40 and 7:53 p.m.