By Maria Golovnina

ALMATY, May 25 (Reuters) - A standoff between Kazakh President Nursultan Nazarbayev and his powerful son-in-law is part of a push by the wily leader to further tighten his control over the elite, investors and diplomats said on Friday.

In a rare public show of internal divisions, Nazarbayev this week ordered a criminal probe into son-in-law Rakhat Aliyev, a longtime ally who has fallen out of favour with the veteran leader in the oil-rich Central Asian state.

Currently ambassador to Vienna, Aliyev has kept a low profile as the authorities seized his media assets on Thursday.

"There has been a slow erosion of influence of this person over the past year ... This is almost the final step in that," said one Western investor who closely watches Kazakh affairs.

Most insiders and analysts agreed the events were part of a broader process to consolidate power in Nazarbayev's hands -- a move his allies say would ensure stability.

Kazakhstan is Central Asia's biggest economy which aspires to join the world's top 10 oil producers in a decade. It sees itself as the region's most stable country and has attracted billions of dollars in foreign investment.

Aliyev, married to Nazarbayev's eldest daughter Dariga, has accumulated vast political and business weight in the former Soviet state since the mid-1990s.

Aliyev, 44, told Reuters in an interview in February he owns 10 percent of international sugar company Sucden, as well as various other interests including KTK TV channel, the popular Karavan weekly and the Kazakhstan Today news agency.

On Thursday, authorities took KTK off the air and closed Karavan for three months citing legal violations. Police are investigating Aliyev on suspicion of kidnapping two executives of Nurbank -- a mid-size Kazakh bank he controls.

His wife Dariga, seen as a possible successor to her father, sought to appear neutral when she told Kazakhstan Today on Monday that "the whole story around Nurbank is the act of those who do not like those far-reaching changes that are taking place in the country at the moment".

Showing the level of investor concerns over the case, spreads on Nurbank's <NRBN.KZ> two Eurobonds were the highest among all Kazakh Eurobonds on Friday. <0#KZEUROSAZ=>

"Mr Aliyev has always stood separately among the Kazakh elite, not only because of his close relation to the president but also due to his, so to say, peculiar way of conducting business," the independent Republic newspaper wrote on Friday.

CLANS AND ELITES

Aliyev has already served one earlier stint as Kazakhstan's envoy to Austria. Government sources say both spells in Vienna are linked to his falling out with the president. Some called his latest appointment a "luxury exile".

"The whole relationship between different groups of the elite is very much at the heart of it all," said a senior Western diplomat in Kazakhstan.

Nazarbayev's move against his son-in-law could shift the balance of power in the often murky world of the Kazakh elite, where other key players are Dariga and another son-in-law, Timur Kulibayev.

The move came days after Nazarbayev signed constitutional amendments allowing him to stay in office for life.

Aliyev's father Mukhtar had publicly spoken against prolonging Nazarbayev's rule.

Exposing a rift in the family, Dariga has publicly praised the reform.

The opposition has condemned the changes as undemocratic.

Commenting on the suspension of Aliyev's media assets, the International Press Institute said in a statement: "This is a politically motivated assault on the media."

But investors were less sceptical.

"Anything that diminishes this person's influence and increases the other person's influence is seen as positive by investors," said the Western investor.

"But obviously if there is any massive concentration of power in one person's hands then of course people will start worrying about what that person's intentions are." (Additional reporting by Olzhas Auyezov)

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