The Australian ended practice third fastest behind Kvyat just 0.5s adrift of the pacesetting Mercedes of Hamilton.
Although an engine failure ended his day prematurely, Ricciardo is confident Red Bull can remain the second quickest team at the Hungaroring.
The 26-year-old will not incur a grid drop penalty as the failure occurred on an older Renault power unit.
“It was one of our better Fridays. We're looking more competitive,” said Ricciardo.
“We've a few updates, and the circuit is one that suits our car, more than the others we've been to this year.
“To have good pace in both sessions, with both cars, is good. On low fuel we're more or less there, and with high fuel it's also looking good.
“The long run looked good before the failure, and my engineer told me we were quickest on track with the soft tyre.
“I didn't expect us to be this close to Mercedes, but let's see what happens in qualifying tomorrow (Saturday).
“Maybe they had a bit more fuel and they will turn it up.
“I just hope we stay where we are. I expect Rosberg to get back in front of us, but if we can be the second best team then that would be a really good day.”
Meanwhile, Red Bull boss Christian Horner has confirmed the team is not expected to receive an updated Renault power unit until October's Russian Grand Prix.
“I don't think anything is scheduled now before Sochi,” said Horner.
“That is probably going to be the earliest we will see any form of development or use of tokens.
“So the engines we have at the moment are what we have to live with for the time being.
“Engines four and five are what the drivers have been using between Friday and Sunday racing.
“Unfortunately, Ricciardo has lost engine four, so he has only got engine five which came into service for the first time in Austria to get him through the next few races.”