La Liga president Javier Tebas said Thursday criminal action could be taken over threats which saw Ukrainian international Roman Zozulya cut short his loan spell at Rayo Vallecano after just one day.

Zozulya joined Madrid-based Rayo on Tuesday from Real Betis on a six-month loan deal, but returned to Betis on Wednesday after being met with protests by Rayo fans over his political affiliations.

A joint statement made by Rayo, La Liga and the players' union AFE on Thursday said Zozulya will decide on Monday whether to return to Rayo after receiving assurances regarding his safety.

"Together La Liga, Rayo Vallecano and AFE want to affirm they are together on this matter and maintain a position that they will not cede to certain pressures," read a statement from the three parties.

"An agreement has been reached to guarantee the safety of the player in both his professional and personal life."

In a letter to Rayo fans, Zozulya admitted to having collaborated with the Ukrainian army during the ongoing conflict with Russian forces in his homeland.

However, he denied having any "link to or supporting any paramilitary or Neo-Nazi group."

"If in my future conversations it is shown that there was clear coercion or if the president of Rayo and the player tell me they have been threatened, I will launch a criminal complaint for coercion," said Tebas.

Zozulya was met with the banners reading "Vallekas is not the place for Nazis" at Rayo's training ground on Wednesday by the club's ultra-left wing supporters' group.

The rest of the Betis squad showed their support for Zozulya in a joint statement on Thursday.

"We are here to express our indignation at the events that our teammate Roman Zozulya has suffered in the past few hours," said Betis captain Joaquin surrounded by the rest of the squad.

"We have witnessed a public lynching of a footballer whose professionalism and personal behaviour has been impeccable since his arrival."

Zozulya has made six appearances for Betis since joining on a free transfer from Dnipro Dnipropetrovsk at the start of the season.

However, he will be unable to play for Betis for the rest of the season despite returning as his registration has been ceded to Rayo for six months.

The 27-year-old claimed in his letter to Rayo fans on Wednesday that accusations of his far-right beliefs come from a misunderstanding of a symbol he wore on a t-shirt upon his arrival in Seville to sign for Betis.

He has received support from Ukrainian tennis player Sergiy Stakhovsky, who shocked Roger Federer at Wimbledon in 2013, and the Ukraine embassy in Spain.

"Dear ultras of @RVMOficial - Looks like you are uneducated, close minded individuals. Your club don't deserve a player like @zozulyaroman18," Stakhovsky posted on his Twitter account.

"Roman Zozulya is one of the Ukrainian patriots who supports the Ukrainian army in their fight against the aggressor for the territorial integrity of our country," the Ukrainian embassy said in a statement.

"We are very proud to have in Ukraine such brave and patriotic young people like Roman Zozulya.

"For this reason we consider the accusations against our compatriot unjust, who is defending his country."