The Hammers' 2-1 loss at Hull on Saturday was their fourth successive Premier League defeat and left the club just six points above the drop zone.
Bilic's side have not won since the 3-1 victory at Southampton on February 4 and the West Ham boss said further speculation over his future was inevitable after the latest defeat at the KCOM Stadium.
But West Ham have moved quickly to quash any uncertainty over Bilic's position and say his job is under no threat.
A statement from the board on the club website read: "To end speculation once and for all, the West Ham United Board feel it necessary to announce that we have 100 per cent faith in Slaven Bilic's ability to lead West Ham United.
"Despite press speculation to the contrary, the manager's position is not under threat. The Board know that Slaven and his coaching staff have the full backing of the playing squad and the overwhelming majority of supporters to lead West Ham United out of this difficult spell.
"The Board now urge all supporters to unite behind the manager, his staff and the squad as we go into some important games. We all have complete confidence in their ability to end a testing run of results and finish the season on a high."
Bilic admitted in his latest Standard Sport column that recent criticism of his side’s performance have got to him.
He wrote: "I don’t blame journalists for asking the questions about my future but what more can I say?"
"Even last season, after things had gone so well, I was consistent. My focus as manager of West Ham United has always been — and always will be — on the team and the challenge ahead. Everything else will take its course.
"If I allow criticism, speculation or anything else to divert my attention from striving to help this team improve, then I am not doing my job.
"I am not on social media, so I don’t see it. I am aware, though, of some of the speculation regarding my position at the club but I have to keep a clear head for the job.
"However, I am human. Anyone who tells you criticism doesn’t affect them is not telling the truth but does it affect my energy or my concentration? No."