The former Oasis frontman said he has “never put my hands on any woman in a vicious manner”, while Gwyther attacked a “pack of lies”.
The Sun reported that Gallagher, 45, had “lost control” during an argument with his partner at London’s Chiltern Firehouse hotel and restaurant, a favourite celebrity hangout.
A source told the newspaper: “He was aggressively pushing her down the corridor.
“Then he stopped and turned away and she started to follow him.
“He suddenly wheeled round, reached out and pushed her by the throat with one hand while holding what looked like a bottle of beer in the other.”
Gallagher was also reported to have shouted: “She is a witch. It was her fault. She is a witch. She is a f***ing witch.”
Commenting on the allegations on Saturday, Gallagher posted on Twitter: “Firstly I have never put my hands on any woman in a vicious manner Secondly there is only 1 witch and we all know who that is as you were LG x”
Gwyther used her Instagram account to release a statement, which read: “The Sun have surpassed themselves yet again.
“Shame on them and on all who have asked for Liam’s comment rather than mine. Caring individuals all of them I’m sure.
“Pack of lies as per usual… ‘Former personal assistant’ being amongst the offensive.
“They’ve taken a couple of years off my age though… journalism at its best! Lazy, sexist nonsense… legal case impending.”
She also told the Sunday People: “Our relationship is stronger than ever. Liam has never laid a hand on me. It is completely ridiculous.”
The Sun on Sunday has since published footage of the alleged incident, a decision the newspaper said was taken following the couple’s denials.
Katie Ghose, chief executive of domestic violence charity Women’s Aid, wrote in the newspaper: “It is shocking to see a man grab his partner by the throat, especially someone as well-known and admired as Liam Gallagher.
“While this is only seconds of film, it is never acceptable to put your hands to your partner’s throat.”
Gwyther, who works as Gallagher’s agent and manager, has been in a relationship with the rock musician following his divorce from singer Nicole Appleton in 2014.
Gallagher has two sons from his first marriage to actress Patsy Kensit and his marriage to Appleton.
He also has two daughters from two previous relationships.
Sky News has contacted Gwyther for comment following the publication of the video.
The Met Police said they are aware of the The Sun footage but a Scotland Yard spokesman told Sky News: “No allegation has been received at this time.”
Chiltern Firehouse has been asked for comment.