The bill is part of an ongoing campaign to halt the trade, after an apparent victory ended in defeat.
Legislation which stopped agricultural authorities providing the mandatory meat inspections was, it was thought, going to bring the trade to an end earlier this year.
However, authorities accepted a proposal from the three plants that they pay to have their inspections carried out.
The bill is sponsored by Republicans John Sweeney, of New York, and Ed Whitfield, of Kentucky.
Two of the plants operate in Texas, the third in Illinois. The meat is exported for human consumption. Most of the horses going to slaughter are young and healthy.
Opponents have argued that the horses are humanely euthanized and that the fate is better than starvation and neglect.
The bill, which would also prevent the export of horses to Canada and Mexico for slaughter, at present has 201 supporters.
The proposed new law does not directly stop slaughtering, but, with bans on trading in horses for human consumption, as well as shipping horse meat intended for human consumption, the law would bring the trade to an end.