Rumours had been circulating locally that the plan might be in jeopardy since Labour lost its place as the largest group on the council.
Although leadership of the council is still to be decided, the Liberal Democrat group has met and reaffirmed its backing for the £100m development, opposite the existing Ninian Park ground.
Group leader Rodney Berman said he had been in contact with club chairman Sam Hammam.
Mr Berman said: "As far as we are concerned the policy of the council on this issue should not change."
The club wants a new home to replace Ninian Park, with seating for 30,000 fans initially - and potentially for 60,000 later - along with a retail park, hotel and health spa.
Mr Berman said the Liberal Democrats recognised the economic benefits to Cardiff of securing Premiership football and the "crucial part" a new stadium would play.
He said that he was "greatly reassured" that there would appear to be no barriers to the deal moving forward, provided the club submits a viable business plan to the council as previously agreed.
Mr Berman said that fans could "rest assured" that his party was "on the case."
He added: "They should not be distracted by scare-mongering from certain individuals who are now clearly putting their own political agenda ahead of the best interests of the fans and the residents of Cardiff as a whole."
Meanwhile, it was announced on Wednesday that Mr Hammam will not be investigated by the data protection watchdog over claims that he helped the former council leader Russell Goodway in the recent local elections.
Mr Hammam sent a letter to more than 20,000 fans urging them to support Mr Goodway.
But the information commissioner branded his comments "a PR exercise", and said he wouldn't be pursuing the matter any further.