The FIA is not ruling out penalties, after stewards on Sunday investigated Mercedes' secret Barcelona tyre test.
Before the Monaco grand prix, Red Bull and Ferrari filed an official protest, arguing the three-day test with a 2013-spec car was a breach of the sporting rules.
Having conducted an investigation after Sunday's race, the FIA confirmed it knew Pirelli wanted to do the test, but only gave a conditional green light in the event "every team is offered the opportunity" to also test.
"The FIA received no confirmation that all teams had been given an opportunity to take part in this test," the FIA statement added.
F1's governing body is not ruling out the intervention now of the International Tribunal, which could "inflict penalties".
Mercedes' Niki Lauda, however, told Brazil's O Estado de S.Paulo that the FIA "sent a delegate" to the test, and that Charlie Whiting and Bernie Ecclestone knew about it as well.
A Pirelli spokesman said Ferrari was invited to test and turned down the offer, while Dr Helmut Marko said a Red Bull engineer had also been "informally" asked.
It is rumoured that Red Bull and Ferrari both said no because they believed the test would have to be done with a two-year old car.
Indeed, between Bahrain and China, a Pirelli tyre test took place with a 2010 Ferrari.
But "Every team would like an exclusive test with a current car," Red Bull team boss Christian Horner said on Sunday.
Sauber team boss Monisha Kaltenborn told Auto Motor und Sport: "We knew nothing about it (the Mercedes test)."
But Mercedes' executive director Toto Wolff denies the team tried to hide the test, and dismissed suggestions the German squad used the opportunity to test car developments.
"There was only ten days between the request and the test," he said, "which is not enough time to produce any development parts."
And Mercedes chairman Niki Lauda insisted: "When we were asked to do this, our team boss Ross Brawn called Charlie Whiting and asked if a test is compatible with the sporting regulations.
"Charlie consulted with the FIA lawyers and gave us the green light. Moreover, Pirelli didn't just ask us, but Red Bull as well."
Christian Horner confirmed that Red Bull was asked by Pirelli. "We declined," he said, "because we are of the opinion that such a test violates the regulations."
Wolff, however, is livid, particularly as the storm coincided with Nico Rosberg's convincing victory in Monaco.
"The term 'sore losers' comes to mind," he is quoted by Speed Week.
But the question remains: did Mercedes unfairly benefit from the exclusive test?
"Impossible to say," quadruple world champion Alain Prost told France's RMC Sport, "but I don't think we can say this win was because of the test. That wouldn't be fair.
"What is certain is that unauthorised things are not allowed. Time will tell," the great Frenchman added.
'Secret test' gave Mercedes a second - Marko
Dr Helmut Marko says Mercedes could have gained a one second per lap advantage by testing between the Spanish and Monaco grands prix.
A controversy has erupted over Mercedes' 'secret' three-day, 1000km tyre test in Barcelona, before Nico Rosberg strolled from pole to victory in Monaco.
Red Bull's Marko told German broadcaster Sky that Pirelli did not ask the world champion team if it wanted to conduct the running.
"We are very unhappy," said the Austrian. "When we test for three days, we go a second faster -- that's what Adrian Newey says.
"It definitely helped them -- you can see that they had no tyre problems today. That's no accident," added Marko.
Red Bull and Ferrari have lodged an official protest, which is being heard by the FIA in the immediate aftermath of the Monaco grand prix.
"There are sporting regulations," said Marko, "that cannot be overriden by a civil agreement between Pirelli and the FIA.
"The sporting regulations state clearly when and how you can test."
He said Red Bull is seeking "a clarification of how to proceed in the future, and that the competitive advantage of Mercedes is compensated in some way".
Massa to recover in time for Canada
Felipe Massa left hospital following checks on Sunday and should be fit for the Canadian grand prix in two weeks.
Whilst already suffering from a sore neck from his practice crash, the Brazilian suffered a near-identical incident during the Monaco grand prix.
After initially recovering trackside in a neck brace, Massa was transferred to hospital for checks but later Tweeted a thumbs-up photo from his Monaco apartment.
"He is fine," said Ferrari team boss Stefano Domenicali, "and I believe that in the space of a few days he will back in perfect shape and ready to race in Montreal."
Although Massa's two Ste Devote crashes this weekend were almost identical, Ferrari believes the first was caused by hitting a bump.
And "It seems that (Sunday's) incident can be attributed to a problem on the left front corner of the car," said technical director Pat Fry.
Money and driver trouble for Lotus
Lotus has recorded the biggest financial loss in motor racing history, according to F1 business journalist Christian Sylt.
A report in the Telegraph said the Enstone based team's latest accounts show an almost $86 million loss for 2012, due to declining sponsorship.
"No other F1 team filing publicly-available accounts has ever lost as much money," said Sylt.
There could be more bad news around the corner for Lotus, amid continuing rumours top driver Kimi Raikkonen could jump ship to Red Bull at the end of the year.
"That would be a shame for Lotus," F1 legend Alain Prost told Welt am Sonntag newspaper, "because he has done a great job for them. But it's his decision."
At the same time, Raikkonen's teammate Romain Grosjean is back in the wars, this time penalised ten places on the Montreal grid for crashing into Daniel Ricciardo on Sunday.
Double world champion Mika Hakkinen is not impressed.
"I think patting him on the head is not working anymore," the Finn told MTV3 broadcaster. "Something is going to happen and I'm sure the team is thinking about what to do."
Hakkinen's former McLaren teammate David Coulthard agrees: "It just goes to show speed is not enough.
"He's done a lot of damage and I don't think Lotus are flush with money," he said on BBC television. "They don't expect four crashes (in one weekend)."
Lotus, however, was also complaining about an erratic driver, following Sergio Perez's feisty race in the McLaren.
Raikkonen called the Mexican "stupid" and an "idiot" after their run-in at the chicane.
"Actually that (idiot) is a nice word compared with what he really said," said team boss Eric Boullier.
Pirelli 'approaching' 2014 F1 contract - president
Pirelli is closer to inking a deal to stay in formula one beyond 2013, following a meeting in Monaco.
After Paul Hembery warned that Pirelli could quit F1 due to the delayed negotiations, Spain's AS sports newspaper reports that Pirelli president Marco Tronchetti Provera met with Bernie Ecclestone.
"We are approaching the conditions (to sign)," Provera said, "so we'll see.
"The fact is that Bernie is happy with us and also our company is still interested in the F1 project, so I hope we can get to an agreement soon and all will be well," he added.
Tronchetti Provera said he is proud of Pirelli's contribution to the sport so far.
"We were asked to add more 'show' to the races, and I think the races are better now than before our arrival, so I think in that sense we have succeeded," he insisted.
As for the controversy caused by Pirelli's heavily degrading compounds in 2013, he explained: "We have developed the tyres with a car several years old, and with not enough days of testing."
Meanwhile, it seems Pirelli will introduce some changes to its tyre design for Canada in two weeks after all, despite the opposition of some teams, including Force India.
"I did it like the old days," Bernie Ecclestone is quoted by Germany's Auto Motor und Sport. "I told the teams that they should be united.
"Pirelli will modify its tyres as planned," the F1 chief executive revealed.