For the six months to June 28 pre-tax profit fell to £8.3m compared with £10.6m on a 2.5% rise in turnover to £614m.
Chief executive, Patrick Macdonald, said that newspaper sales had increased due to the "tabloid cover price war".
He said: "Magazine sales were up 3.6% reflecting strong partwork sales and the launch of new titles in the women’s interest sector.
"Phonecards, which are low margin, were down £2.5m reflecting the growth of electronic top-up."
With regard to the code of practice for the supply of newspapers, Menzies said it would work with all sides to ensure the UK network continues to provide "the most efficient and economic route for the distribution of this most time-sensitive product".