This follows the Hampshire police charging 11 people with indecent chanting following homophobic comments aimed at Pompey's former Spurs defender Sol Campbell during the match at Fratton Park in September.
Spurs boss Harry Redknapp also moved from Fratton Park to the North-London club recently and tensions are bound to be high.
"We would urge supporters to observe the club code of behaviour at matches," said a statement from Spurs.
"The unacceptable chanting which marred our visit to Fratton Park in September resulted in several arrests and it is in the interests of everyone associated with the club that we do not have a repeat of that regrettable incident.
"The club does not tolerate abusive, offensive or obscene chanting, including anything of a homophobic nature.
"The behaviour of fans will be under the spotlight at this match.
"We shall take action against anyone seen or heard to be guilty of any such offence.
"We have previously banned individuals due to unacceptable behaviour - please do not put us in the position where we are forced to take such action.
"Full houses at the Lane have always provided terrific inspiration to the team and this will be vital on Sunday.
"Please focus your energies on cheering your team to victory."
Pompey, meanwhile, have urged their 1,700 travelling fans not to "let the club down."
"The indecent abuse directed at Pompey captain Sol Campbell by Spurs supporters when the sides met at Fratton Park in September - and subsequent police action - meant the return fixture in north London was already under the microscope," read a club statement.
"With the possibility of heightened tension we implore our travelling supporters to maintain their excellent reputation as ambassadors for Portsmouth Football Club.
"In a meeting with Pompey last week, the safety team at White Hart Lane spoke highly of the behaviour of travelling Blues fans on past visits.
"We do not want that opinion to change.
"Any fans involved in indecent chanting or disorder will be dealt with by Portsmouth Football Club, with the possibility of a lifetime ban. They will also be dealt with by the police.
"Please don't let your club down."