Top officers told the Guardian its stories were exaggerated without revealing they had hired former NoW deputy editor

Scotland Yard's most senior officers tried to convince the Guardian during two private meetings that its coverage of phone hacking was exaggerated and incorrect without revealing they had hired Neil Wallis, the former deputy editor of the News of the World, as an adviser.

The first meeting in December 2009, which included the Metropolitan police commissioner Paul Stephenson, was two months after Wallis was employed by the Yard as a public relations consultant.

Wallis, 60, who was deputy to Andy Coulson, the NoW editor at the time of the phone hacking, was arrested on Thursday as part of Operation Weeting. Coulson has also been arrested and bailed.

Theresa May, the home secretary, has referred Scotland Yard's hiring of Wallis to the judicial inquiry on phone hacking which will be chaired by Lord Justice Leveson.

During the meetings in December 2009 and February 2010, which also involved the assistant commissioner John Yates and the force's director of public affairs, Dick Fedorcio, the senior officers said articles written by Nick Davies about phone hacking were incorrect, inaccurate and wrongly implied the force was "party to a conspiracy".

Alan Rusbridger, editor-in-chief of the Guardian, has written to Fedorcio about failing to mention that the Yard was being advised by Coulson's former deputy.

In the letter Rusbridger wrote: "Paul Stephenson and you came in to meet me and Paul Johnson [deputy editor] in my office on 10 December 2009. Among the things we discussed was the commissioner's strong feeling that Nick Davies's coverage of phone hacking was overegged and incorrect.

"In February 2010 you wrote to me complaining that another Nick Davies story 'once again presents an inaccurate position from our perspective and continues to imply this case has not been handled properly and we are party to a conspiracy' ... You suggested a follow-up meeting with Assistant Commissioner John Yates.

"That meeting took place on 19 February. John Yates also tried to persuade us that Nick's doggedness and persistence in pursuing the story was misplaced."

The letter ends with Rusbridger posing five questions to the Met: "Why did you not think it appropriate to tell me at the time of these meetings that you, Paul and John were being advised by Coulson's former deputy?

"What advice did he give you about the coverage of phone hacking?

"Was Wallis consulted in advance of these meetings or subsequently informed of the nature or contents of our discussions?

"Why did you think it was appropriate to hire Wallis, given his closeness to events which the Guardian and other media organisations were reporting at the time?

"What conversations – formal or informal – did you, Paul or John have with Wallis about the subject of the NoW and phone hacking during the period he was working?"

Fedorcio, who has held his post since 1997, has been invited to testify before MPs on the home affairs committee on Tuesday.

A Metropolitan police spokesman said it could not comment on why it did not mention Wallis's employment in the private meetings at the Guardian. Because of the judicial inquiry, it would not comment on why it was thought appropriate to hire Wallis, nor could it comment on any formal or informal conversations Stephenson or Yates had with the former Murdoch executive while he worked part-time at the Yard.

The spokesman denied that Wallis had been consulted about phone hacking or gave any advice about it, in their first on-the-record denial: "He was not involved in any operational activity and that includes giving any advice on phone hacking."