The US has the most cases, and more than 1,000 died there in the past day.
The disease, Covid-19, first emerged in central China three months ago.
Though the tally kept by Johns Hopkins records one million confirmed cases, the actual number is thought to be much higher.
It took a month and a half for the first 100,000 cases to be registered. A million was reached after a doubling in cases over the past week.
Nearly a quarter of cases have been registered in the United States, while Europe accounts for around half.
The pandemic is taking a huge economic toll: an extra 6.6 million Americans applied for unemployment benefit last week.
The US has reported 1,169 deaths in 24 hours - the highest daily death toll of any country so far.
Earlier, Spain said 950 people had died in a day, which is a record number for Europe in this outbreak.
The number of confirmed Spanish cases rose from 102,136 on Wednesday to 110,238 - an 8% rise that is similar to the rate recorded in previous days. Authorities believe the virus is now peaking and say they expect to see a drop in figures in the days ahead.
"We continue with an increase of around 8%. This points, as we have already seen, to a stabilisation in the data that we're registering," said María José Sierra, from the Spanish health ministry's emergency co-ordination unit.
Spain, the worst-hit nation after Italy in terms of deaths, has also lost nearly 900,000 jobs since mid-March.
In other developments:
The commander of the USS Theodore Roosevelt has been removed after saying the US Navy was not doing enough to halt a coronavirus outbreak on board the aircraft carrier
The Zaandam cruise ship, with dozens of ill passengers on board, docked in Florida after several South American countries refused to accept it
New York mayor Bill de Blasio urged all of the city's residents to cover their faces when outside and near others, with a scarf or bandana, rather than a surgical mask, as medics need the latter
The World Bank approved a plan to disburse $160bn (£130bn) in emergency aid over 15 months to help countries stricken by the pandemic
The French authorities have boosted police checks to prevent anyone trying to go on holiday this weekend ahead of Easter
UK Health Secretary Matt Hancock said the aim was 100,000 tests a day in England by the end of April amid criticism of the government's plans
A 4,000-bed emergency field hospital at London's ExCel centre is due to open later