As many as 150 text messages exchanged between David Cameron and former News International chief Rebekah Brooks over a number of months "could prove to be a considerable embarrassment to the government" according to weekend reports.
Reports appeared in the Observer and the Mail on Sunday with the Observer giving the 150 figure. The texts were described variously as " intimate" , "salacious" and "embarrassing."
The existence of the messages has been at the centre of a row between Labour MP Chris Bryant and Cameron for several weeks, said the Observer.
In one message, Cameron thanks Brooks for letting him ride one of her family's horses, saying it was "fast, unpredictable and hard to control but fun", it is claimed.
In another Brooks is said to have told the Tory leader that she felt so emotional listening to his conference speech she "cried twice", adding: "Will love 'working together'."
Brooks is to stand trial next year on charges of phone hacking and conspiracy to pervert the course of justice.
These two messages are part of a cache of texts and emails between Downing Street and Brooks handed over to Lord Justice Leveson's inquiry into media ethics by Downing Street and Brooks.
Bryant has confirmed he has written to Leveson demanding that he publish all the texts and emails between the pair.
The Observer said it understood there may have been as many as 150 messages exchanged between the two over a number of months, "many of which would prove to be a considerable embarrassment to the government".
Cameron rejected a demand in the Commons by Bryant two weeks ago to disclose all the texts and emails exchanged with Brooks, whose husband, the racehorse trainer Charlie Brooks, has been a friend since both attended Eton.
Both texts revealed on Saturday are said to have been sent in October 2009, shortly after Brooks left her job as editor of the Sun and became chief executive of News International.
The Observer said the texts shed further light on the extraordinarily close relationship between Cameron and Brooks, both members of the "Chipping Norton set" based around their Oxfordshire homes.
Cameron and Brooks met 22 times in a six-year period. Brooks has said that at the height of the phone-hacking scandal he sent her a morale-boosting "keep your head up" message, and expressed his regret he could not be more loyal to her in public.
The Mail on Sunday report said David Cameron was accused by Bryant of withholding "more than 130 text and email exchanges with Rebekah Brooks – as Downing Street insisted it didn’t possess a single one."
Bryant said he was talking of texts and emails never sent to the Leveson Inquiry.
He claimed he had spoken to a mole in No 10 about the messages and accused the PM of seeking to conceal them because they are ‘salacious and far more embarrassing’.
A Downing Street official insisted NO messages were handed over because none were found when officials searched the No 10 telephone archives.
The MoS said an explanation could be that the computer system used to archive Cameron’s mobile has not stored his texts properly since friends of Mrs Brooks say she was in regular text contact with him. An alternative is that Cameron used a different private mobile, said the MoS.
Bryant demanded publication of all the texts and emails, because he believes it is ‘material’ what contact Cameron had with News International officials other than just about the BSkyB bid.
He said: "The Leveson Inquiry is meant to refer to the whole of the relationship between the police, the Press and politicians and I think most ordinary members of the public would think that it is material whether the Prime Minister was texting Rebekah Brooks every day or just once every two years."