France are joined in second place by Spain, with Germany still fourth.
The only other changes in the top 10 were Argentina (fifth) swapping places with the Netherlands (sixth) and Denmark moving up from 11th to joint 10th with the United States.
England (seventh), Turkey (eighth) and Mexico (ninth) remained unchanged, while Costa Rica, up to 18th last month, climbed a further place to 17th, their highest ever position.
The biggest movers were Georgia, who rose nine places to 84th following their 1-0 Euro 2004 qualifying victory over Russia on April 30.
Bhutan moved into the top 200 for the first time, climbing five places to 195 thanks to a 6-0 victory over Guam in the Asian Nations Cup preliminary competition.
Montserrat remained 204th and bottom of the list, which is based on a rolling analysis of results over the last eight years weighted on the strength of the opponents and the importance of each match.
Leading rankings (April's position in brackets):
1. (1) Brazil 843 points
2= (3) France 784
2= (2) Spain 784
4. (4) Germany 757
5. (6) Argentina 753
6. (5) Netherlands 746
7. (7) England 739
8. (8) Turkey 722
9. (9) Mexico 720
10= (10) United States 715
10= (11) Denmark 715
12. (14) Italy 709
13. (13) Czech Republic 707
14. (12) Portugal 706
15. (15) Ireland 704
16. (16) Belgium 681
17. (18) Costa Rica 671
18. (17) Cameroon 666
19. (19) Paraguay 664
20. (20) Sweden 660