* Cameron is first British PM to visit Kazakhstan
* British leader wants business deals, help on Afghanistan
* Activists say he must raise human rights issues too
By Andrew Osborn
ATYRAU, Kazakhstan, June 30 (Reuters) - British PrimeMinister David Cameron flew into Kazakhstan on Sunday to helpinaugurate the world's costliest oil project and seal newbusiness deals, but faced immediate pressure to denounce thecountry's poor human rights record.
Cameron's visit, the first by a serving British primeminister, is seen by the Central Asian government as a coup ithopes will cement its status as a rising economic power andconfer a degree of legitimacy from the West it has long sought.
It comes just days before the 73rd birthday of PresidentNursultan Nazarbayev, who has ruled the former Soviet republicwith a tight grip for over two decades.
Former British prime minister Tony Blair's consultancy firmalready advises Nazarbayev, a former Communist party apparatchikwho tolerates no dissent or opposition.
"We are very honoured and privileged to have such attentionon the part of two prime ministers - Tony Blair and DavidCameron," Kazakh Foreign Minister Erlan Idrissov told reportersin a phone call before the visit.
"We cherish and enjoy the support of developed countries."
Cameron, who is accompanied by a British businessdelegation, is expected to oversee the signing of about a dozencontracts involving British firms and to cut the ribbon oninfrastructure elements of the Kashagan offshore oilfield.
Royal Dutch Shell has a 16.81 percent stake in the facility,which is in the Kazakh segment of the Caspian Sea. Nazarbayevsaid last week consortium members had so far invested $48billion, making it the most expensive oil venture in the world.
It is due to produce its first oil in September.
Cameron is also hoping to persuade Kazakhstan to expandtransit rights for British military forces relocating equipmentfrom Afghanistan between now and a planned withdrawal next year.Nazarbayev has already granted overflight rights, but Cameron islooking for land transit rights too.
As Britain's trade with the euro zone suffers because of thecurrency bloc's debt woes, it is looking further afield to forgebusiness links with countries that have enjoyed rapid economicgrowth in recent years.
TEMPTING TARGET
With a $200 billion economy, the largest in Central Asia,and deep oil and gas reserves, Kazakhstan is a tempting target.Britain is already among the top three sources of foreign directinvestment, according to Kazakh officials.
Since its 1991 independence, officials say British firmshave invested about $20 billion in their economy, part of atotal $170 billion ploughed into Kazakhstan since then.
But more high profile trade links carry political risks.
New York-based Human Rights Watch said Cameron had a duty touse his trip to denounce human rights abuses.
"We are very concerned about the serious and deterioratinghuman rights situation there in recent years, including credibleallegations of torture, the imprisonment of government critics,(and) tight controls over the media and freedom of expressionand association," it said in a letter on Friday.
Cameron told reporters in Islamabad on Sunday he never shiedaway from having difficult conversations on such trips.
"In all the relationships we have there's never anything offthe table and we raise and discuss all these issues, and thatwill be the case with Kazakhstan as well," he said.
"It is important to make this visit. It's very muchsomething I chose and wanted to do."
Kazakhstan was a key market for British firms, he added,saying that other European leaders had visited and it was "hightime" a British prime minister did too.
In another awkward twist for Cameron, the London-baseddaughter of a jailed former Kazakh businessman, MukhtarDzhakishev, has urged him to raise her father's case when hemeets Nazarbayev.
But it is the case of Vladimir Kozlov, a jailed oppositionleader, that activists most want Cameron to mention.
An outspoken critic of Nazarbayev, Kozlov was jailed forseven-and-a-half years in October for colluding with a fugitivebillionaire in a failed attempt to rally oil workers to bringdown the government. Kozlov denied the charges.
Idrissov, the foreign minister, said criticism of hiscountry was overdone.
"We do not claim that we have got everything right," hesaid. "It was never going to be possible to turn a country withno democratic institutions or culture into a Jeffersoniandemocracy in two decades." (Additional reporting by Dmitry Solovyov; in Almaty; Editing byAndrew Heavens)