VIENNA (Reuters) -Austria plans to tighten its gun control rules after a 21-year-old killed 10 people then killed himself in the country's worst school shooting by far, the conservative-led government said on Wednesday.

The gunman, a former pupil at the school in the southern city of Graz, owned the two firearms he used in his rampage, a shotgun and a Glock pistol, legally. 

Under the current rules, the shotgun can be bought by any adult who has not been banned from owning weapons, after a wait of three working days. The Glock requires a gun permit, for which one must be 21 or over and pass a psychological test.

After a cabinet meeting, the government said it would raise the minimum age for a gun permit to 25 from 21, make the psychological test more stringent and increase the "cooling off phase" for all weapons to four weeks.

"We ... promised that we would not go back to business as usual and that we would draw the right conclusions from this crime to live up to the responsibility we have," Chancellor Christian Stocker told a joint press conference with the leaders of the two other parties in the ruling coalition.

"Today's cabinet decision shows that we are fulfilling that responsibility," he said.

The school shooter, identified by Austrian media as Arthur A., failed the psychological test that is part of the screening for military service, but the armed forces are not currently allowed to share that information. 

The government plans to ensure such information is shared and taken into account in applications for gun permits, it said in a statement issued after the press conference. Newly issued gun permits will also expire after eight years, it added.

The government said it planned to introduce a separate gun permit for those under 25 that would apply to the category of weapons that includes the shotgun the shooter used, but a spokesman said details were still being ironed out.

Beyond gun ownership rules, the government plans to increase psychological counselling and monitoring at schools as well as ensure a greater police presence in front of schools until the end of the school year, Stocker said.     

(Reporting by Francois Murphy, Editing by Louise Heavens)