Internal Security Minister Gideon Ezra offered to help organize a friendly match between Betar Jerusalem and Bnei Sakhnin in an attempt to make peace between the rival teams.
On Sunday night Betar and Sakhnin fans clashed with each other and the police following a goalless Premier League match at the Doha Stadium in Sakhnin.
Fans, who threw stones and punches and damaged parts of the newly opened stadium, later blamed the 350 policemen at the stadium for standing by idly and not taking action to prevent the violence.
On Tuesday Ezra spoke with Israeli Football Association chairman Itche Menahem and offered to provide free police security if the friendly match was to go ahead.
The IFA pays for police security at matches and Ezra's offer was viewed as an attempt by the police to make up for its mishandling of the game's security.
Ezra's office said that Bnei Sakhnin accepted his offer and that Betar Jerusalem was considering it. The venue has yet to be confirmed although it is believed that Menahem would like to hold the game in Sakhnin.
Representatives of both clubs are due to appear at an IFA disciplinary hearing Wednesday to discuss the actions of the fans at Sunday's match.
Menahem told The Jerusalem Post that he intends to discuss the possibility of a friendly game with officials of both clubs at the disciplinary meeting.
"There was a conversation between myself and Gideon Ezra about a friendly match and I think it is a good idea," Menahem said. "I hope and believe it is possible to make a peace between the two teams. It is not possible to [feud] all the time."
Betar president Vladimir Shklar confirmed that he spoke to Menahem about the option of a friendly game. However he said Betar's general manager Luis Fernandez is unsure whether it will be possible to fit the extra game into the team's already busy schedule.
"Luis Fernandez said it would not be good professionally because we have many games in the coming months," Shklar said.
"Itche Menahem said he was thinking of holding it in the next couple of weeks but we already have league games, Israeli Cup games and Toto Cup games. If the friendly is not held within two weeks I don't believe it will happen."
Despite the obvious hatred between many fans of Bnei Sakhnin and Betar, Shklar said he believed a friendly could help iron out the differences.
"Every thing that can bring peace between the fans is good. We need to try to make peace between the two sides," he said.
Galilee Police on Tuesday arrested three residents of Sakhnin who allegedly participated in the Sunday night riots.
Meanwhile, the company that built the Doha Stadium announced Tuesday plans to build an extra section, which they claim will help prevent crowd violence.
The stadium currently hosts 5,000 fans, housed on one side of the pitch and behind one goal. The new $4 million stand, to be completed by the start of next season, would be constructed along the other side allowing room for an extra 4,000 supporters.
Project manager Yaron Golan, from the Gadish construction company, said: "Increasing the capacity of seats in the stadium will enable creating a clear separation between the home and visiting supporters in sensitive games."
Golan also spoke of plans to improve security at the stadium including adding closed circuit television systems, and widening the sterile area in the entrance for the inspection of supporters.