The team will celebrate its 100th race in its current guise in Canada this weekend.
It is currently fifth in the constructors' championship, ahead of McLaren. It finished fourth in Bahrain with Paul di Resta and fifth in Monaco with Adrian Sutil.
"I think we are now knocking on the door of our first podium finish since 2009, and it's time to do that all-important step," said Mallya.
"Montreal would be a great place to do so - it is a track that favours overtaking and our car has shown the race pace to finish among the leaders, so everything is possible.
"I am proud of everyone in the team because we have achieved good results - and claimed 44 points – despite some very unfortunate occurrences.
"With a bit more luck, we would be even further ahead of McLaren: but the focus is on the future.
"We know our rivals will be more competitive in the next few rounds, but we have shown we can mix with the big teams and we intend to do so for the coming races too."
Mallya underlined that when he took over what was then the Spyker team prior to the 2008 season, it was mired at the back of the field.
"When we started back in 2008 we simply had the ambition to break out of Q1 and we dreamed of scoring points," he said.
"Seeing where we stand today is therefore extremely rewarding and motivates us all to continue working just as hard for the next 100 races."
- Sports & Recreation
- Motor Racing
- Paul di Resta