BAKU (Reuters) - The government of Azeri President Ilham Aliyev should begin liberal economic and political reform now or it will run the risk of instability in the tightly controlled ex-Soviet republic as oil revenues drop, a leading think tank said. The International Crisis Group said Aliyev had surpassed his late father and long-serving leader Heydar in the level of control he exerts over society in mainly Muslim Azerbaijan, where oil-driven economic growth has helped ensure stability. This stability, however, has come with the consolidation of authoritarian rule, greater suppression of freedoms and an increased reliance by elites on corruption and patronage networks to dominate virtually all aspects of public life, the Brussels-based group said in a report released late on Friday. Oil revenues are levelling off and are projected to decline within a few years, potentially leading to economic problems and growing public frustration with the closed political system, the report warned. The growing over-reliance on the energy sector, discrepancies in wealth distribution and public disenchantment with both the government and traditional opposition parties increase the likelihood of a surge in radicalism and instability in the medium to long term. It is in the regimes own interest to open up political space, take steps to rein in corruption and de-monopolise the economy, while it stands on solid financial and political ground, the report said. Since succeeding his father as president in 2003, rights groups say Aliyev has presided over increasingly stringent curbs on democratic freedoms under cover of an oil-fuelled economic boom. The government, which is locked in a festering conflict with Armenia over the rebel region of Nagorno-Karabakh, denies quashing dissent and points to rapid economic growth in recent years that it says has made Aliyev genuinely popular. The country of 8.3 million people, sandwiched between Russia, Iran and Turkey, holds a parliamentary election on Nov. 7 almost certain to confirm the overwhelming dominance of the ruling Yeni (New) Azerbaijan Party. The opposition accuses the West of muting its criticism of the Aliyev regime for fear of losing out to Russia in the competition over Azeri energy resources in the Caspian Sea. Azerbaijan hosts oil majors including BP, ExxonMobil and Chevron.