Martino has come under fire in the Catalonian press following a 3-1 defeat to Real Sociedad last weekend, which left Barca three points adrift of Real Madrid in the La Liga title race.
The 51-year-old was sent to the stands during that loss and is banned from the technical area for Sunday's visit of Almeria.
There has been speculation that the Argentinian, who took over from Tito Vilanova in July, will leave Camp Nou at the end of the season.
However, Bartomeu told Catalonian television station 8TV: "We are very pleased with Tata Martino. We do not consider that he does not continue with Barcelona."
Bartomeu is refusing to panic following the reverse against Sociedad, and is confident that Martino's side will be in the running for honours at the end of the campaign.
"(The league) is not won in the month February," Bartomeu added.
"These players have shown that they can be in all finals. (But) they also have bad games."
