Anderson has been charged under Level 3 of the ICC Code of Conduct for Players and Player Support Personnel by India team manager Sunil Dev following the alleged incident that took place on the second day of the match at Trent Bridge last Thursday.
If proved guilty, Anderson will face a ban of two to four Tests and four to eight ODIs.
England and Wales Cricket Board, however, said it has lodged a code of conduct violation by Jadeja.
According to an ICC statement, it is alleged that this was a continuation of a verbal altercation between Anderson and Jadeja as they were walking from the field.
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Level 3 charges are referred to a Judicial Commissioner for adjudication. As such, where required under Article 5.2 of the ICC Code of Conduct for Players and Player Support Personnel, the ICC will appoint a Judicial Commissioner who will hold a hearing as soon as reasonably practicable, the statement further said.
In response, the England and Wales Cricket Board (ECB) said it has notified the ICC of its intention to lodge code of conduct breaches against Jadeja.
James Anderson categorically denies the accusations made against him and the ECB has pledged their total support for the player should he be charged by ICC.