* Authorities see growing criminal activity in Ukraine
* Fear Russia could use this to discredit "Maidan" revolt
By Richard Balmforth
KIEV, April 1 (Reuters) - Ukraine's parliament on Tuesday ordered security forces to disarm illegal armed groups as police shut down the Kiev base of a far-right nationalist group prominent in the overthrow of Viktor Yanukovich after a shooting incident in which three people were wounded.
Ukraine's new leaders acted after Monday night's violence in Kiev city centre, conscious that an increasing criminal climate could discredit the anti-Yanukovich uprising and be used by Moscow's propaganda machine to show that law and order was breaking down in Ukraine.
The proposal approved by parliament linked a growing "criminal atmosphere" to what it described as "systematic provocations from foreign citizens in the eastern-southern regions of Ukraine and in Kiev" - suggesting that Russian agents or trouble-makers were stirring unrest in parts of the country.
"Parliament orders the interior ministry and the state security service to immediately disarm illegal armed groups," the motion said.
"Only those in the armed forces of Ukraine, the National Guard or the state security service (SBU) may carry arms," said acting president Oleksander Turchinov. "If they do not belong to the army, the National Guard or the police, they are saboteurs who are working against Ukraine."
Police on Monday night moved in on a city centre hotel where the far-right group Right Sector had its Kiev base after a man - said by police to be a member of the group - pulled out a gun and shot and wounded three people outside a restaurant.
The incident occurred close to Independence Square or Maidan, centre of the uprising against Yanukovich. He fled in late February after a three-month revolt in which more than 100 people were killed, many by police snipers.
Right Sector was the first group on the side of the protesters to use violent tactics against Yanukovich's riot police - including throwing petrol bombs and bricks and burning police vehicles - in otherwise peaceful 'Euromaidan' demonstrations against Yanukovich.
But the continued activity of the group long after the flight of Yanukovich risks embarrassing the new leadership as it tries to foster a peaceful and orderly climate around a presidential election on May 25.
They are aware that Russia, which has annexed Crimea, has an interest in projecting an image of lawlessness in Ukraine as it now presses proposals for Ukraine to become a federation with Russian a second state language alongside Ukrainian.
A 33-year-old suspect was detained by police in connection with the shooting, the interior ministry said.
Right Sector members later left their headquarters in the hotel without arms and were driven away by police to their bases outside the capital after an appeal for them to given themselves up, interim Interior Minister Arsen Avakov said on his Facebook page.
Police found several weapons in a search at the hotel, a separate statement by the interior ministry said.
"Checks are being made on whether they were used in other crimes," it said.
Relations between the authorities and Right Sector have grown more tense since a prominent group member, nicknamed Sashko Bily, was shot dead on March 24 when police from the 'Sokol' special unit moved in to arrest him in the western Ukrainian region of Rivne.
(Additional reporting by Natalia Zinets; Writing By Richard Balmforth; Editing by Angus MacSwan)