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Elite sport in Britain returned without fans last month after a near three-month shutdown due to the Covid-19 pandemic and the government is set to allow spectators at carefully selected trial events from late July to early August.
Arteta, whose positive test for Covid-19 led to the suspension of all elite soccer matches in England in March, said patience was key in bringing supporters back.
"Things are evolving in different countries in different ways. We're all desperate to have our people back in the stadium and make football what it is," Arteta told reporters ahead of Saturday's FA Cup semi-final against Manchester City.
"We need to be able to create a safe environment for everyone to come and join. My opinion is it will be gradual and the sooner the better, but let's be careful."
City boss Pep Guardiola welcomed the decision but stressed the importance of fan safety.
"This is the most important thing, we miss the fans... but they have to be safe," Guardiola said.
Hopefully the authorities can allow people back when the security is right, that's the most important thing."
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Tottenham Hotspur coach Jose Mourinho said opening stadiums to fans, even if it was to a limited capacity to adhere to social distancing protocols, would be a "good start".
"Everybody who loves football wants football for all. Us living from football, making our salaries from football, knows the importance of that," he said. "I think we would all be so, so happy to see people back at stadiums."
Southampton's Ralph Hasenhuettl said reopening stadiums was "fantastic" news.
"It will be a big message for everybody because this is a step back to normality, even if it's only half of the crowd that is coming back," he said.
"We'd like to see them back and we can show them good performances and we'd like to celebrate again with the fans."