West Ham banned a season-ticket holder and promised action against other offenders after chanting in November's match at White Hart Lane which Spurs won 3-1.
"We have made it very clear that we will not tolerate any form of discriminatory behaviour and one by one we will root out those fans that do not deserve to represent this great club of ours," West Ham joint chairmen David Sullivan and David Gold said on the club's website.
"We must be clear that we will pursue the harshest sanctions against any individual who goes against what we stand for as a club."
During the November match there were reports of West Ham fans chanting "Adolf Hitler, he's coming for you", and hissing, mimicking the gassing of Jews during the Holocaust.
Tottenham have strong Jewish ties.
At the same game there were also reports of West Ham fans chanting "Viva Lazio" and "Can we stab you every week?" in relation to an attack on Spurs fans in Rome ahead of a Europa League match with Lazio.
Spurs said in a statement on their website that police had asked them to remind supporters that the behaviour of both sets of fans would be under scrutiny.
"The club does not tolerate discrimination of any sort, on the pitch or in the stands, and we shall take action against anyone heard using abusive, offensive or obscene language," Tottenham's statement said.
"All of our supporters travelling to Upton Park are doing so as ambassadors of the club and we would ask that they behave in a manner of which we can be proud."
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