The International Automobile Federation (FIA) said it had opened a process "to identify a candidate team to participate at a competitive level" from the start of 2016 or 2017 until at least 2020.
Details of the selection criteria and process will be revealed to those registering their interest by June 30, and paying an initial non-refundable fee of $5,000.
Full applications should be submitted by Sept 1 with a decision expected on Sept 30. The total application fee was set at $130,000.
Formula One currently has 10 teams, with some of them struggling financially. The American-based Haas team is due to join next year as the 11th -- if all of the others survive.
The sport has not had 12 teams, and 24 cars, since the end of 2012.
Three new teams joined in 2010 but only one is still competing -- the Manor Marussia outfit that went into administration and missed the last three races of 2014.
Caterham folded at the end of last season while HRT ceased to exist after 2012.
However, the sport's commercial supremo Bernie Ecclestone said a year ago, after the last such tender, that Formula One had agreed to accept two new teams with one of them being Haas.
The FIA said all new applicants would be expected to undergo thorough due diligence and satisfy them as to their technical ability and resources.
The governing body said it would also assess the value that any new team could bring to the championship, and it would not select a team if it deemed none were viable.
(Reporting by Alan Baldwin, editing by Tom Hayward)
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