VIENNA (Reuters) - Thousands of shops across Austria will reopen on Tuesday as it becomes one of the first countries in Europe to loosen its coronavirus lockdown, but the government is still telling the nation it is "not out of the woods" yet.

Austria acted early in its outbreak to close schools, bars, theatres, restaurants, non-essential shops and other gathering places roughly four weeks ago. It has told the public to stay home and work from there if possible.

It has fared relatively well so far, having reported 368 deaths in total, fewer than some larger European countries have been suffering each day. The daily increase in confirmed cases is in low single digits in percentage terms and hospitalisations have stabilised.

"Economically, too, we want to come out of this crisis as quickly as possible and fight for every job in Austria," Chancellor Sebastian Kurz, a conservative governing with the Greens, said in an open letter to the country on Saturday, the eve of Easter Sunday.

Last week, he outlined a step-by-step plan to reopen parts of the economy, starting with shops of up to 400 square metres (4,300 square feet)- roughly twice the playing area of a singles tennis court - as well as all home-improvement and garden centres on Tuesday.

They are due to be followed by shopping centres, larger shops and hairdressers from May 1. Restaurants and hotels could reopen progressively from mid-May, Kurz has said.

It remains unclear whether, even with limits on the number of people allowed inside shops and a requirement for all shoppers to wear face masks, Kurz is sending a mixed message about the lockdown, which is in place until the end of April.

The World Health Organization on Friday urged caution, saying: "Lifting restrictions could lead to a deadly resurgence", without mentioning Austria specifically.

"I am simply 100% certain that we did the right thing and are doing the right thing," Kurz said in an interview with newspaper Kurier published on Saturday.

The same day, he told national broadcaster ORF: "We are not out of the woods. The danger is still among us," urging the public to keep self-isolating and implement social distancing.

Other Western European countries are loosening their lockdowns, albeit differently. On Monday, Spain allowed some activities, including construction and manufacturing, to restart. Denmark is reopening daycare centres and schools for children from first to fifth grades on Wednesday.

(Reporting by Francois Murphy; Editing by Peter Cooney)