The Manchester United Supporters’ Trust has urged co-chairman Joel Glazer to engage with fans to avoid a repeat of the protest at Old Trafford on Sunday.
United’s Premier League match against Liverpool was called off after about 200 fans broke into the ground.
The Football Association is investigating the incident and said it “understood” fan “frustrations”.
Fans were protesting against owners the Glazers, who MUST says have “driven the club into debt and decline”.
An investigation by Greater Manchester Police is under way into the violent disorder around the protests and a 28-year-old man has been arrested.
Assistant chief constable Nick Bailey said the behaviour “shown at this protest was absolutely atrocious”.
Earlier, MUST said frustrations had reached “boiling point” on Sunday, which had led to the demonstration.
“Not one member of the Glazer family has ever had so much as a conversation with us,” they wrote in an open letter.
Fans have been angered by United’s decision, alongside five fellow Premier League clubs, to join the European Super League (ESL) last month, before subsequently all pulling out.
Joel Glazer “apologised unreservedly” on behalf of the club for their involvement in the ESL but MUST has said it has no trust in the owners.
It is the first time a Premier League match has been postponed because of fan protests.
Police said two officers had been injured during the protests outside the ground.
In a statement, the FA said it “cannot condone the violent and criminal behaviour that took place before the scheduled Manchester United v Liverpool match”.
Earlier on Monday, MUST said it “supported the right of fans to protest lawfully”.
“Although we did not personally witness any such acts, of course we do not condone any acts of violence,” the supporters’ group said.
“None of us want this to continue.”
Some United fans also gathered outside the Lowry Hotel where the players were staying before the match.
The FA will speak to United, the Premier League and safety authorities to find out what happened and the reasons for it.
Manchester United said “criminal damage” caused by protesters breaking into the ground, and “violence towards” staff, other fans and officers were now a police matter.
“The club has no desire to see peaceful protestors punished, but will work with the police to identify those involved in criminal activity, and will also issue its own sanctions to any season-ticket holder or member identified, per the published sanctions policy,” the club said in a statement.
The club also reiterated its willingness to engage with supporters through its “fans forum and other appropriate channels”.
MUST has laid out a four-point plan which it believes will provide a way forward “for all of us”.
It has asked for the club to take part in the government’s fan-led review of football governance and appoint independent directors to the board.
They also want the club to work with MUST and other supporters on a fan share scheme and consult season ticket holders on any significant changes at the club.
“This is the only way to move this issue on. We strongly suggest you take it,” the statement added.
MUST has asked for a public and written response by Friday.