Speaking after the match last weekend, Pulis expressed his anger at the behaviour of Ivanovic and Blues team-mate Oscar in Stoke's 1-0 defeat at Stamford Bridge, branding the pair "laughable" for what he dubbed their "simulation" and saying the issue needed to keep being highlighted.
Chelsea were not awarded any penalties during the contest and midfielder Oscar picked up a booking for diving, but Ivanovic escaped a caution after throwing himself down in the box when he appeared not to be touched.
At a press conference on Thursday morning to preview Stoke's home game against Swansea on Saturday, Pulis discussed the matter again and called on the Football Association to impose three-game bans, making specific reference to Ivanovic.
"I have spoken about simulation before," said Pulis, whose defender Andy Wilkinson is serving a three-match suspension for a violent conduct charge brought against him by the FA following an incident in a game against Manchester City on September 15.
"They are really quick to pull people up on incidents that they think are bookable or sending-off incidents, and I think they should pull people up for diving and give them a three-game ban straight away.
"Ivanovic would be looking at three games, Chelsea wouldn't be too happy with him and I don't think he would be diving around any more.
"We just don't think it's right and we encourage the players to be as honest as they can.
"Kights (Potters winger Michael Kightly) stayed on his feet (in a separate incident) and rightly so.
"We think it is the way to do it - whatever other clubs do, they do."