Formula 1 teams have been promised that the 2021 engine regulations will be firmed up by the end of next month.
Liberty officials and the FIA met with teams on Friday to conduct the second round of talks over the 2021 rules.
Pirelli is understood to have been absent but FIA president Jean Todt was in attendance having missed the original presentation from F1 chiefs in Bahrain.
Economic aspects dominated the meeting but the future engine regulations were also discussed, with Todt expressing a firm deadline of the end of June after an initial target of May.
Zak Brown, the CEO of McLaren's F1 team, said he was encouraged by Todt's commitment "because we were looking for some definitive timelines".
He added: "Now I think all the teams are anxious to see not only the engine regulations put in place but the balance of the governance, the economics, the sporting, to follow quickly, because we all need to adapt quickly to what will clearly be a new Formula 1 in 2021."
F1's next engine regulations are the most time-sensitive element but the hope is that progress defining other parts such as the governance of F1 and a budget cap will follow.
Renault Sport F1 boss Cyril Abiteboul suggested to Sky Sports F1 it would be a "couple of weeks, if not months" before teams get a full set of regulations.
Another key part of F1's planned 2021 overhaul is a budget cap, mooted to be $150million.
Simpler aerodynamic rules and standardisation of some car components would facilitate a need for a smaller headcount and allow teams to operate on less expenditure.
F1 sporting boss Ross Brawn has made clear that these changes would not necessarily put hundreds of people out of work, as they would be able to join teams that are currently less-resourced.
The likes of Sauber, Toro Rosso and Force India will still probably have scope to increase their staff counts, providing potential homes for employees at bigger teams that could be left redundant.
In the meeting, it was suggested to teams that bigger organisations could progressively reach a reduced staffing figure over a few seasons from 2021, instead of immediately having to adhere to a limit.
Mercedes motorsport boss Toto Wolff said it was important that Liberty had acknowledged a cost cap is "a process, not an event".
"This was a very good point," said Wolff. "It needs to go over several years, and it needs to consider the various structures that are being put in place.
"They are taking our feedback onboard."
Brown said McLaren could redeploy staff to other programmes, especially as it is reviewing possible World Endurance Championship and IndyCar campaigns.
He added: "We're a nimble racing team, a large organisation, and we will be well suited to react to whatever rules are implemented.
"But that's why we want to know sooner rather than later so we can start making the right plans."