Speaking to tabloid Bild, Meuthen said that his party colleagues had failed to properly prepare for the meeting with Aiman Mazyek, president of the Central Council of Muslims.
“With a meeting like this you need to clearly define what will be discussed, that clearly wasn't the case” he said.
Meuthen was not present at the meeting, which was attended by Petry and party colleagues Albrecht Glaser and Armin-Paul Hampel.
Mazyek had invited Petry to talks after AfD members voted for a party manifesto earlier this month calling for a series of measures targeted at Islam, including bans on minarets and face veils being worn in public.
The Muslim leader had labelled the AfD “Nazis” in response to the leadership's plans before they were confirmed by members at a party congress and said he hoped to use the meeting to convince Petry to withdraw those parts of the platform.
Petry told reporters on Monday that she broke off the meeting after Mazyek refused to withdraw his comparison between the AfD and the Third Reich.
Glaser confirmed to Bild that the three AfD representatives had agreed among themselves before the meeting that they would not discuss any other issues before Mazyek withdrew the comparison.
“That was the entrance that Aiman Mazyek had to pass through before we would talk about things with content with him,” he said.
Mazyek told the Rheinische Post he is still open to discussions “with reasonable members of the AfD.”