* Medvedev says security in Chechnya has improved
* Chechen leader Kadyrov says has subdued rebels
* Medvedev hopes for new investment, jobs
(Changes source, adds details, background)
By Oleg Shchedrov
MOSCOW, March 27 (Reuters) - Russian President Dmitry Medvedev said on Friday that improved security in Chechnya meant it was time to review tight restrictions in force there for the past decade.
Restrictions such as curfews, roadblocks, periodic searches and easier detention rules were imposed in Chechnya in 1999 when Russia sent troops to the region to end its short-lived independence, won in an earlier war with Moscow.
Kremlin opponents say the special regime, which includes restricted access for journalists, has encouraged massive rights violations in the region.
"I believe there is a need to consider the question of the legal regime now in force in Chechnya under the anti-terrorism operation," Medvedev said at a meeting with the head of Russia's Federal Security Service, Alexander Bortnikov.
The National Anti-Terrorism Committee, which Bortnikov also heads, should consider the issue and report to the government, he said. Parliament has the final say.
In the past 10 years the pro-Moscow regional administration led by former rebel Ramzan Kadyrov has subdued large-scale rebel resistance.
Chechnya today is stable compared with North Caucasus neighbours like Ingushetia and Dagestan, which face a growing Islamic insurgency.
Kadyrov, who rules Chechnya with an iron fist and has long wanted to ease both the restrictions and Moscow's grip on the region, praised Medvedev's remarks.
"It should rather be viewed as an acknowledgement of the fact that the problem of fighting illegal armed formations has been finally solved in the Chechen republic," he said in a statement read by his press secretary by telephone.
Kadyrov said lifting the restrictions would encourage the return of Chechen emigrants who had fled during the two wars. "Our compatriots see positive changes. People may return home."
Kadyrov has also tried to take over police and security forces in the region, currently controlled from Moscow.
Russia has withdrawn most of its troops from Chechnya, leaving only two brigades. Police detachments from all over Russia operate in Chechnya on a rotating basis, but Kadyrov said this would stop because local forces could manage.
Chechnya remains one of Russia's poorest regions, dependent on handouts from the federal budget. Seizing control of the local economy and Moscow's cash cements Kadyrov's authority.
Medvedev said Russia would not slacken its campaign against terrorism in the region. "We should on the one hand create new opportunities for people, for attracting investment, creating new jobs ... on the other hand we should consistently and resolutely fight terrorists." (Writing by Oleg Shchedrov, additional reporting by Aydar Buribayev, editing by Tim Pearce)