“I’m appealing to you to stay out of trouble,” Hodgson said in a video message. “We really desperately want to stay in the competition.”
Rooney told fans: “Be safe, be sensible and continue with your great support for the players.”
Violence in Marseille overshadowed England’s 1-1 draw with Russia and European governing body UEFA threatened to kick both teams out of the tournament if the disorder continued.
It also said both countries must make an appeal to their fans not to cause unrest.
England play rivals Wales in the northern French city of Lens on Thursday and Russian fans will also be in the area as their team face Slovakia in nearby Lille a day earlier.
In a video message posted on the English Football Association’s Twitter feed, Hodgson said: “As England manager I’m obviously very concerned about the threat which is now hanging over us and the sanctions that could possibly be imposed upon the England team.
“We worked very hard to get here and we really desperately want to stay in the competition. I’m appealing therefore to all of our fans.
“We appreciate your support at all our matches, of course, but I’m appealing to you to stay out of trouble and to try and make certain that these threats that are being issued are never carried out.”
🎥 A message to #ThreeLions fans from #ENG manager Roy Hodgson and captain @WayneRooney #TogetherForEngland https://t.co/dXRSZdMUXk
— England (@England) June 13, 2016
Following Hodgson, Rooney said: “I’d like to thank the England fans for the great support inside the stadium against Russia and now we have a big game coming up against Wales.
“I’d like to ask the fans, please, if you don’t have a ticket, don’t travel, and for the fans with tickets, be safe, be sensible, and continue with your great support for the players. Thank you.”
The FA’s chief executive, Martin Glenn, said on Sunday that the warning from UEFA was being treated with the “utmost seriousness”.
“We understand the potential implications of our supporters’ actions and wholly accept that every effort needs to be made by the FA to positively urge them to act in a responsible and respectful way,” he added.
The Russian Football Union has also issued a warning to fans, urging them to “show respect to the opponent and its fans” and “follow the laws and rules of conduct and public order in France”.
Prior to the tournament, England and Wales were advised to base themselves in Lille for Thursday’s game, rather than Lens, which is the smallest of the 10 host cities.
Assistant Chief Constable Mark Roberts, head of Britain’s policing operation for the tournament, said it was “realistic to expect” that Russian fans in Lille will “try to behave in a similar way”.
He told The Daily Telegraph newspaper: “They will be in Lille the night before and people should just bear that in mind.”
The violence in Marseille, which left one English supporter in a critical condition and 10 people facing trial, unsettled the families of some England players.
Rebekah Vardy, wife of Leicester City striker Jamie, tweeted that she had been caught up by “horrific” violence prior to the Russia game.
“That has to be up there with the worst experience EVER at an away game!” she wrote. “Teargassed for no reason, caged and treated like animals! Shocking!”
