Martial has struggled for form, scoring just one goal in his past six appearances across all competitions – against League Two side Tranmere Rovers in the FA Cup last month.
The 24-year-old failed to fire for United in Sunday's (AEDT) goalless Premier League draw at home to Wolves, but Solskjaer backed the Frenchman.
"He's giving us everything. I think he's started the last eight games in this month, and he's running probably 20 per cent more than what he did when I came here," Solskjaer said.
"That shift goes with all the other players as well, by the way. So it's not just mental robustness and tactical, it's that physical side we've had to work with, because they are making strides. But the difference in that, compared to when I came in, the squad weren't right.
"We'll give him [Martial] more support, give him rest when he deserves it. If he does have that rest, if he plays a little bit less - because he's been asked to play too much as well, especially now when Marcus [Rashford] is injured - as a striker, if you don't just get there that split second, that's a big, massive difference.
"I've praised him, I've sat down with him and I'm delighted with him. I know that he's tired, but he's never ever dodged a training session. He's training, he's available for every game, so I’m delighted with the boy."
Martial has scored eight Premier League goals in 19 matches, and 12 in all competitions this season.