British football must stop the current handshake row from becoming a "mafia feud", says Professional Footballers' Association chief Gordon Taylor.
Anton Ferdinand refused to shake the hand of John Terry on Saturday following allegations Terry made racist comments to Ferdinand last season.
Taylor told BBC Radio 5 live: "We have to move on. These things will separate us and become like some mafia feud."
The 67-year-old also insisted pre-match handshakes should remain.
He said that "owners, managers, chief executives and players" had agreed to the goodwill gesture when it was brought into the Premier League in 2008-09 and saw no reason why it should be ditched now.
"I would like to say to the players that I see no reason why they cannot do it," said Taylor.
"They are not betraying any personal principles. It is being done for the image of the game and to set the right example to the mascots and youngsters playing at school."
There have been a number of high-profile incidents following the introduction of the pre-match handshake.
In February 2010, Manchester City left-back Wayne Bridge refused the hand of former England and Chelsea team-mate Terry following allegations of an affair between Terry and Bridge's ex-girlfriend.
Two years later, Liverpool striker Luis Suarez turned away from Patrice Evra before the league clash between Manchester United and Liverpool.
Suarez had served an eight-match ban for racially abusing the France left-back in a previous encounter.
United and Liverpool are due to meet at Anfield on Sunday. So far, there has been no request for the pre-match handshake to be cancelled.
Speaking on Match of the Day 2 on Sunday, Dion Dublin said football authorities should "do away" with enforced handshakes and said Ferdinand and Terry had been "forced" to shake hands against their will.
"I think it is wrong," said the former England and Manchester United striker. "If you have play against an opponent, after the game shake their hand. Leave them to deal with the situation themselves."
Terry was accused of racially abusing fellow defender Ferdinand during a Premier League match last October. The Chelsea man was cleared in court but faces an FA charge later this month.
Handshakes were abandoned in the return league game between the west London clubs last season, as well as before their FA Cup tie.