By Stephanie Nebehay

GENEVA (Reuters) - United Nations human rights experts called on Kenya on Thursday to investigate fully all cases of violence after 2007 elections and denounced a "climate of impunity" still shielding suspects.

Kenya should "as a matter of urgency, pursue all cases of post-2007 election violence to ensure that the perpetrators are brought to justice and that victims are adequately compensated", the U.N. Human Rights Committee said.

The Hague-based International Criminal Court said on July 9 that four prominent Kenyans, including presidential hopefuls Uhuru Kenyatta and William Ruto, would be tried for masterminding the 2007/2008 bloodshed that killed more than 1,200. All deny wrongdoing.

Their trials for crimes against humanity were set for April 2013, a month after Kenyatta and Ruto intend to stand in a presidential election in east Africa's largest economy.

"There are cases of a high level pending before the ICC with regard to these events. But there are a large number of middle- and low-level perpetrators who are below the radar of the ICC," committee member Gerald Neuman told a news briefing.

"Kenya needs to accelerate the process of dealing with these cases in order to avoid impunity," he said.

"Some cases have been brought, small numbers, but what is going to happen to the rest of the files is a matter of concern."

Human Rights Watch, in a report last December, accused the country's political elite and police of stalling investigations.

The U.N. committee voiced concern "at the slow pace of investigations and prosecutions into allegations of torture, extrajudicial killings by the police and by vigilante groups".

It also urged Kenya to boost security at camps of Somali refugees and investigate "physical and sexual violence by the police towards refugees" that erupted after bombs killed police officers last December.

"The refugees need to be comprehensively protected, but unfortunately they also need to be protected against the people who are there to protect them," Neuman said.

(Editing by Andrew Roche)