UKIP MEPs Steven Woolfe and Mike Hookem have been reported to French police over their altercation at the European Parliament.
Martin Schulz, the president of the European Parliament, has referred the matter to the French authorities because of "the seriousness of the reported facts and their possible criminal implications".
He told MEPs: "it has been concluded that the versions of the facts given by the two members involved diverged substantially and the facts seem to have happened in the absence of direct witnesses.
"It also [has to be] stressed that given the seriousness of the reported facts and their possible criminal implications, further evidence is needed to clarify this matter.
"As a result I have decided to follow the recommendation of the advisory committee and I have referred this matter to the competent French authorities.
"Based on the result of the investigations I will then take a decision about a sanction to be imposed."