The detained are all members of Spain's far-right Patriotic Socialist Movement and they were arrested after they attacked doormen at the hotel who were trying to prevent them from entering, a police spokesman said.
Four people were lightly injured in the scuffle but did not require medical care, he added.
The National Democracy Party which staged the event said it had requested police protection because of fears that far-left groups might try to disrupt it as has happened in the past.
It was not immediately clear why members of the Patriotic Socialist Movement tried to disrupt the event, which featured in addition to Griffin, the leader of Italian far-right party Forza Nuova, Roberto Fiore, and National Democracy leader Manuel Canduela.
In June Griffin and another BNP member won seats in the European Parliament elections, a first for the party which advocates the voluntary repatriation of immigrants. It has no seats in the national parliament.
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Two far right groups came to blows outside the Velázquez Hotel in the capital
28 people were arrested in Madrid on Saturday when two far right groups came to blows outside the hotel Velázquez in the city.
All the arrests were from the far right collective Patriotic Socialist Movement, who were trying to break up a meeting being held inside the hotel by the D.N., Democracia Nacional group.
The meeting had invited the Euro MP and leader of the British Nationalist Party, Nick Griffin, to talk, along with Roberto Fiore from Forza Nuova and Manuel Canduela from the DN.
The Democracia Nacional group had asked for police protection to, as they put it, ‘avoid the usual violent episodes that so called anti-system groups arrange every time the DM or its president carries out any act’.
Statements were taken from those arrested at the headquarters of the Police Provincial Information Brigade.
Several people needed medical attention after the riot.
A Spokesman for Nick Griffin told the Daily Telegraph that he ‘may’ have made a visit to Franco’s tomb at the Valley of the Fallen.
Friday the 20th was the 34th anniversary of Franco’s death.