As another day in the extraordinary saga drew to a close, there was no formal word from the ECB as to whether they had received an apology from Pietersen.
Earlier, Strauss entered the debate over the omission of Pietersen, saying he regretted "dirty laundry'' being aired in public.
"I've always got on with Kevin,'' Strauss told Sky Sports. "I've tried to be honest with him; he's been honest with me.
"That's why this has all been a bit of a surprise to me.
"I think the discontent that Kevin had with the board over his contract situation was one that the players didn't get involved in - and I didn't really get involved in, if I'm honest.
"But over the last week I have had to get involved because there have been issues a little bit more central to his relationship with the other players and our ability to perform out in the middle.''
Strauss added: "I'm a big believer in not airing dirty laundry in public.
"It's one of our core values in our team that what goes on in the dressing room stays in the dressing room.
"Any time anyone has fallen foul of that they have been disciplined - and rightly so.
"It's about mutual respect and trust, and that is a core issue that is central to resolving this.''
Tensions between Pietersen and the England hierarchy have been escalating all summer, with the South Africa-born batsman retiring from limited overs internationals after England refused his wish to opt out of 50-over matches while still playing Twenty20s.
Then came his extraordinary press conference after the Headingley Test, where he speculated the match at Lord's might be his "last Test''.
And last week, on the eve of the squad announcement for Lord's, he took to YouTube to insist he was now available to play for England in all formats.
Meanwhile England's Stuart Broad has insisted he'd no role in a parody Twitter account for Pietersen.
The account - KP Genius - was set up by a friend of Broad, Richard Bailey, and had been thought to have contributed to dressing room tensions, with Pietersen reportedly concerned some of his team-mates were involved.
But all-rounder Broad insisted Tuesday: "I would like to confirm that I had no involvement in this whatsoever.
"As has been widely reported Mr Bailey is a friend of mine, but we had no conversations regarding this issue at all and I am pleased that he has now decided to close the parody account down.''
England, 1-0 down in the three-match series, must win at Lord's if they are to prevent South Africa replacing them as the world's No.1 Test side.
-AAP
