Reporting by David Gruz and Oriol Puigdemont
Suzuki won a MotoGP race as recently as 2016, when Maverick Vinales triumphed at Silverstone, but the team then took a big step backwards last year as it had switched to an all-new line-up of Andrea Iannone and Alex Rins in 2017.
But Suzuki - and Rins in particular - had a positive pre-season prior to 2018, and the Spaniard was third-quickest at the end of Friday at Qatar.
View photos Alex Rins, Team Suzuki MotoGP.
His teammate Iannone was fifth, the Italian finishing ahead of the works Hondas and Yamahas.
Honda rider Marquez, who was sixth-fastest overall, says Suzuki now has to be considered a team that is capable of wins and podiums.
"They are ready to make podiums and even win races," said Marquez.
"I was [riding] behind Rins, both he and the bike can go, so one more rival and someone to keep an eye on."
Marquez added that the opening day at Qatar confirmed that Honda still struggles at the track, and that Ducati's Andrea Dovizioso, who topped the first two practice sessions, is the favourite.
"The Ducatis are going fast. Here the favourite is Dovizioso, he always had great races [in Qatar], not only last year but two or three years ago.
"The Ducati works and [Danilo] Petrucci also made some good tests and will be ahead."
View photos Marc Marquez, Repsol Honda Team. Rins: Suzuki improvement "confirmed"
Rins said that Suzuki's step forward from last year was "confirmed" on Friday, and that his goal for the Qatar Grand Prix is to be able stay with the frontrunners.
"I'm happy with how we started the weekend, I'm calm because it is confirmed that we are good," said Rins.
"We did a big step compared to last year, also in my case I have more confidence with the bike, I have more power in me, more kilometres on the MotoGP bike.
"The truth is that it is not easy because there are many people with good rhythm - Petrucci, Marquez, Dovi, Valentino [Rossi].
"They are very fast riders and everything is very close. The goal is to be with them."