Saturday's 3-0 defeat to Hoffenheim leaves Hamburg 17th in the German top flight, four points clear of bottom side Eintracht Braunschweig.
Hamburg are the only club to have competed in the Bundesliga each season since its inception in 1963 but sit a point off safety after 19 games.
Despite their faltering season, Jarchow insists the club are not ready to dismiss Van Marwijk, who took over from Thorsten Fink in September.
"Even a defeat to (Hertha) Berlin (next weekend) would not change our faith in Van Marwijk," he told Kicker.
"We are pleased that Van Marwijk is in Hamburg."
Jarchow also voiced his displeasure that it was solely Van Marwijk whose position had been called into question, rather than the players.
"We are always changing coaches here and there is talk about the position once again," he continued.
"What annoys me is that the highly paid players are as such taken out of the firing line again."
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