Saturday's 3-0 defeat by Leicester City, in which Newcastle had two players sent off, provoked passionate comments from Carver who suggested Mike Williamson had got himself red-carded deliberately.
It also left the Magpies in dire straights in 15th place in the table, only two points above third from bottom Sunderland who have a game more to play.
They would drop to 16th if Hull City avoid defeat against Arsenal later on Monday.
A statement on the club's website said there had been two days of "frank discussions" with Carver and senior players.
"The outcome of those discussions is that the board, John Carver, his staff and players are absolutely focused on our situation and the three hugely-important fixtures that remain this season, two of which are at St. James' Park," it said.
"All parties accept responsibility for the current situation but are determined, together, to ensure this Club -- your Club -- retains its Premier League status.
"That is the only focus at this time."
Williamson issued a statement on Sunday refuting suggestions that his rash tackle on Leicester's Jamie Vardy when the ball was running out of play had been a deliberate attempt to get sent off and incur a ban.
Carver, 50, stepped up to manager of the first team when Alan Pardew left the club at the turn of the year when they were in the top half of the table.
He has lost 12 of his 17 games in charge in all competitions.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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