Manchester City say they "regret any offence" caused by a number of their supporters singing about the Hillsborough disaster on Saturday.
The club say they are "disappointed" to hear about the latest incidents and state they will continue to work with Liverpool to end the disgraceful chanting.
A statement read: "Manchester City FC are disappointed to have heard inappropriate chants from home fans during today's game.
"We regret any offence these chants may have caused and will continue to work with supporters groups and officials from both clubs to eradicate hateful chanting from this fixture."
Relations between the two fanbases have become increasingly fraught over the last couple of years.
City claimed they banned a number of supporters who were caught on video singing about the Hillsborough deaths after last year's 2-2 draw at the Etihad, while Pep Guardiola apologised after an FA Cup semi final at Wembley that same month.
City fans scrawled graffiti over the concourses of the away end relating to both Hillsborough and the Heysel tragedy during October's 1-0 win for Liverpool at Anfield also.
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