The last of the 11 teams to show off their 2013 car, the former champions had barely started testing the FW35 before it emerged that the sport's governing body disagreed with their interpretation of the rules.
"The team spoke with the FIA this morning which is when they gave us their view," said a spokeswoman at Barcelona's Circuit de Catalunya.
"The team are now seeking further clarification on this and a decision as to whether this design will be carried forward will be made before the first race."
The season starts in Australia on March 17, with one more four-day test scheduled for Barcelona after the current one ends on Friday.
Teams can put all sorts of aerodynamic and technical innovations on their cars in testing with the FIA only declaring them to be 'illegal' once they are presented for grand prix scrutineering.
All teams are constantly seeking advice from the governing body, however, as they search for possible loopholes or seek to deny rivals any suspected advantage.
Caterham have already drawn critical comments from rivals for their exhaust design, with Lotus technical director James Allison saying at the previous test that he expected to see changes before Melbourne.
The FIA concern is believed to be over the use of bodywork behind the exhaust exits that harnesses the gases for aerodynamic advantage.
The technical debate followed a confident rollout by Williams, who won with Venezuelan Pastor Maldonado at the Barcelona track last year.
"Given the rule stability over the winter, I'm pleased with the gains that we've been able to make with this car," said technical director Mike Coughlan. "It's a better, more refined Formula One car than the FW34."
Founder Frank Williams, whose team are the second most successful in terms of constructors' championships (nine) but finished eighth last year, saw a step forward.
"Williams has been at the top many times over the last 30 years. It's the nature of the sport to have ups and downs, but when we are down we always fight our way back," he said.
"I'm hoping that with the current team we have in place... we will be in a position to challenge the very best."
Maldonado has a new team mate this year in Finnish rookie Valtteri Bottas, previously the reserve.
Susie Wolff, wife of shareholder and new Mercedes team executive director Toto, is the development driver and was first to drive the new car in a shakedown at the nearby Idiada track before Maldonado took over for the second pre-season test.
The team said more than 80 percent of the car was new, including the gearbox and rear suspension as well as radiators, floor, the exhausts, bodywork and nose. A "considerable" amount of weight had been saved also.
Reliability work over the winter had been promising, with the gearbox alone completing 3,200km on the dyno at the factory.
"This season we must be even more competitive which I believe is possible," said Maldonado, who got married over the winter break and also has a new race engineer.
"My goal is to help take the team back to the top."
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