Mosley's latest move comes ahead of the British Grand Prix at Silverstone
Max Mosley has written to five of the potential breakaway Formula 1 teams in a fresh attempt to end the row that threatens to divide the sport.
Brawn GP, BMW Sauber, McLaren, Renault and Toyota have all lodged conditional entries to the 2010 championships, dependent on a relaxation of new rules.
World motorsport boss Mosley's latest letter proposes a £86m budget cap for 2010, falling to £39m in 2011.
A deadline of 19 June has been set for teams to agree on the 2010 regulations.
Ferrari, Toro Rosso and Red Bull have refused to race under the optional £40m budget cap originally proposed by Mosley, with only Williams and Force India definitely on the starting grid next season.
Reports have claimed that the new terms offered by the FIA president were virtually agreed upon by the five conditional entrants in recent talks.
But team insiders at Silverstone for this weekend's British Grand Prix have insisted that there was still some distance between the two camps when discussions broke down.
Mosley said the proposed budget limits would be enforced by an independent auditor in an attempt to overcome the teams' reluctance to allow the governing body access to their accounts.
There were also concessions to allow teams to continue with 2009 rules on engines through into next season.
Mosley also intimated that the teams' concerns over the FIA's International Court of Appeal might be resolved.
In exchange, the teams have been asked to continue operating under the terms of the Concorde Agreement that expired in 1998.
This would end the contractual limbo that has existed since the most recent version of the agreement lapsed in 2007 and set out the team's relationship with the FIA until 2014 or the deal is superceded by a new one.
If Mosley's revised offer fails to tempt the wavering teams to meet Friday evening's deadline, the FIA has promised to promote more new outfits into the championship to replace them.
Campos Grand Prix, Manor and US F1 have already been named alongside the current 10 teams on the provisional 2010 entry list.
However the prospect of some of the most famous marques in F1 history decamping to form their own competition could attract leading drivers to follow suit.
A letter from the Formula 1 Teams' Association (Fota) on Wednesday called for a "a reasonable and rapid solution to the outstanding issues".
The FIA has accused some elements with Fota of attempting to "take over the regulation of F1 from the FIA, and to expropriate the commercial rights".
The Fota teams are meeting on Thursday evening to discuss a plan of action ahead of Friday's deadline.