England, the 1966 World Cup winners, exited in the round of 16 after a humiliating defeat to Iceland which saw them drop two places to 13th.
Iceland, the smallest nation ever to have qualified for the European Championship, with a population of 330,000, saw their fairytale run end in the quarter-finals but saw their rankings jump 12 places to 22.
There were no changes in the top five rankings with Copa America finalists Argentina retaining top spot, followed by Belgium, Colombia, Germany and Chile.
Five times World champions Brazil, who failed to progress past the group stages of Copa America for the first time since 1987, are on the brink of dropping out of the top 10, ranked at ninth, ahead of Italy.
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European Championship finalists France jumped 10 places to move to 7th, one place behind winners Portugal.
Top 10 (last month's positions in brackets)
1. Argentina (1)
2. Belgium (2)
3. Colombia (3)
4. Germany (4)
5. Chile (5)
6. Portugal (8)
7. France (17)
8. Spain (6)
9. Brazil (7)
10. Italy (12)
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
