* Third nuclear security summit since 2010 held in The Hague
* Aim to prevent militant groups from obtaining nuclear bomb
* Will meet again in Chicago in 2016
* Analysts see "moderate" steps forward, want bolder action
* Current summit overshadowed by dispute over Ukraine
* Russia, China shun U.S.-led initiative at summit (Adds Dutch, analysts comment, paragraphs 6-7)
By Fredrik Dahl
THE HAGUE, March 25 (Reuters) - World leaders called on countries on Tuesday to cut their use and their stocks of highly enriched nuclear fuel to the minimum to help prevent al Qaeda-style militants from obtaining material for atomic bombs.
Winding up a third nuclear security summit since 2010, this one overshadowed by the Ukraine crisis, 53 countries - including the United States and Russia at a time of high tension between them - agreed much headway had been made in the past four years.
But they also underlined that many challenges remained and stressed the need for increased international cooperation to make sure highly enriched uranium (HEU), plutonium and other radioactive substances do not fall into the wrong hands.
The United States and Russia set aside their differences over Crimea to endorse the meeting's final statement aimed at enhancing nuclear security around the world, together with other big powers including China, France, Germany and Britain.
But Russia, China and 16 other countries shunned a separate initiative of the United States, the Netherlands and South Korea at the summit to incorporate U.N. nuclear agency security guidelines into national rules.
"The absence of Russia, China, Pakistan, and India - all nuclear weapons states with large amounts of nuclear material -as well as others ... weakens the initiative's impact," said the Fissile Materials Working Group (FMWG) of security experts.
The Dutch hosts hailed the summit as "a major step towards a safer world". By contrast, the FMWG said the summit had taken "moderate steps" toward stopping dangerous weapons-usable nuclear materials from going astray but that bolder, more concerted action was needed.
U.S. President Barack Obama said Ukraine's decision at the first nuclear security summit in Washington in 2010 to remove all of its HEU was a "vivid reminder that the more of this material we can secure, the safer all of our countries will be".
"Had that not happened, those dangerous nuclear materials would still be there now," Obama told a news conference. "And the difficult situation we are dealing with in Ukraine today would involve yet another level of concern."
At this year's summit, Belgium and Italy announced that they had shipped out HEU and plutonium to the United States for down-blending into less proliferation-sensitive material or disposal. Japan said it would send hundreds of kilograms (pounds) of such material to the United States.
Like plutonium, uranium can be used to fuel nuclear power plants but also provides the fissile core of a bomb if refined to a high level.
"We encourage states to minimise their stocks of HEU and to keep their stockpile of separated plutonium to the minimum level," said the summit communique, which went further in this respect than the previous summit, in Seoul in 2012.
A fourth meeting will be held in Chicago in 2016, returning to the United States where the process was launched by Obama.
"We still have a lot more work to do to fulfil the ambitious goals we set four years ago to fully secure all nuclear and radiological material, civilian and military," Obama said.
To drive home the importance of being prepared, the hosts sprang a surprise by organising a simulation game for the leaders in which they were asked to react to a fictitious nuclear attack or accident in a made-up state, officials said.
Analysts say that radical groups could theoretically build a crude but deadly nuclear bomb if they had the money, technical knowledge and fissile substances needed.
Obtaining weapons-grade nuclear material - HEU or plutonium - poses the biggest challenge for militants, so it must be kept secure both at civilian and military sites, they say.
Around 2,000 tonnes of highly-radioactive materials are spread across hundreds of sites in 25 countries. Most of the materials is under military control but a significant quantity is stored in less secured civilian locations, the FMWG said.
Since 1991, the number of countries with nuclear weapons-usable material has roughly halved from some 50.
However, more than 120 research and isotope production reactors around the world still use HEU for fuel or targets, many of them with "very modest" security measures, a Harvard Kennedy School report said this month.
"With at least two and possibly three groups having pursued nuclear weapons in the past quarter century, they are not likely to be the last," the report said.
Referring to a push to use low-enriched uranium (LEU) as fuel in research and other reactor types instead of HEU, the summit statement said: "We encourage states to continue to minimise the use of HEU through the conversion of reactor fuel from HEU to LEU, where technically and economically feasible.
"Similarly, we will continue to encourage and support efforts to use non-HEU technologies for the production of radio-isotopes, including financial incentives," it said.
An apple-sized amount of plutonium in a nuclear device and detonated in a highly populated area could instantly kill or wound hundreds of thousands of people, according to the Nuclear Security Governance Experts Group (NSGEG) lobby group.
But a so-called "dirty bomb" is seen as a more likely threat than an atomic bomb: conventional explosives are used to disperse radiation from a radioactive source, which can be found in hospitals or other places that may not be very well secured.
In December, Mexican police found a truck they suspected was stolen by common thieves and which carried a radioactive medical material that could have provided such an ingredient.
In another incident that put nuclear security in the spotlight and embarrassed U.S. officials, an elderly nun and two peace activists have admitted breaking into a Tennessee defence facility in 2012 where uranium for atomic bombs is stored. (Editing by Mark Heinrich)