Travellers from most European countries will be allowed into Italy from Wednesday, with no quarantine.
Italy is also lifting restrictions on domestic travel, allowing people to move between regions.
The UK government defends its 14-day quarantine for travellers, which begins on Monday.
The Lancet "raises concern" about a hydroxychloroquine study that caused the WHO to suspend trials.
Brazil's death toll exceeds 30,000, the highest in South America.
Globally, there have been almost 6.4m confirmed cases and 379,000 deaths.
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