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Austria could start easing its coronavirus lockdown measures from next week, Chancellor Sebastian Kurz said Monday, but warned that this depended on citizens abiding by social distancing rules.

"The aim is that from April 14... smaller shops up to a size of 400 square metres, as well as hardware and garden stores can open again, under strict security conditions of course," Kurz said at a press conference.

He said that as of April 14, the current obligation to cover one's mouth and nose in supermarkets will be extended to other shops and on public transport.

He added that if the government's timetable goes to plan, larger shops will reopen on May 1.

From mid-May hotels, restaurants and other services could also start to open their doors again in stages, Kurz said, adding that a decision on this would be taken at the end of April.

'Strongest decline in EU'

However, he said that the restrictions on movement that Austria has introduced to fight the spread of COVID-19 remained in place.

He urged Austrians not to celebrate Easter with people outside their household, adding that he would not be seeing his own parents.

Schools will remain closed until at least mid-May and public events will remain banned until the end of June.

If trends in infection begin to worsen again, the government "always has the possibility to hit the emergency brake" and re-introduce restrictions, Kurz said.

He pointed to the example of Singapore, which initially had managed to contain the spread of the virus but was now facing a second wave of infections.

Kurz also warned that international travel would continue to be severely hampered for the foreseeable future, with discussions ongoing at an EU level as to how restrictions could be eased.

Kurz was speaking alongside several cabinet colleagues who entered wearing face masks before taking them off to speak behind specially erected screens.

Reopening parks

Interior Minister Karl Nehammer announced that the government also hoped to re-open public parks on April 14.

He clarified that the punishment for not adhering to mask-wearing in shops and on public transport would be 50 euros ($54).

Health Minister Rudolf Anschober said he was encouraged by the downward trend in the growth rate for infections, adding: "We have the strongest coronavirus decline in the EU".

The country of 8.8 million people currently has 12,058 confirmed infections, with 204 deaths and 2,998 recoveries.

In mid-March the increase in infections was running at around 40 percent, which unchecked would have led to two million people in Austria contracting the virus by now, Anschober said.

The daily rate of increase is now at 1.6 percent with a successful flattening of the curve, Anschober said, although he emphasised the rate must be brought down yet further.

Anschober also welcomed the fact that Austria was "well ahead" of many other countries when it comes to testing, with 111,000 tests carried out so far.

He said that great progress was being made on antibody tests and that he hoped these could be used in infection "hotspots".

Also on Monday authorities in western Tyrol, Austria's worst hit region, said that the quarantine ordered for the region's 750,000 people would be lifted on Tuesday.