(Adds quotes from U.N. investigator, no comment from Geneva police)

By Tom Miles

GENEVA, June 24 (Reuters) - Swiss police were guarding three U.N. investigators into Eritrea's human rights record in Geneva on Wednesday after a top official said they had received threats on the street and at their hotel.

The inquiry's report published earlier this month showed human rights violations in Eritrea that may amount to crimes against humanity, including extrajudicial killings, widespread torture and enforced labour.

As the investigators began testimony before the U.N. Human Rights Council, council president Joachim Ruecker told the session they had been subjected to "various threats and acts of intimidation in their hotel and in the streets since their arrival in Geneva".

He said security had been redoubled, the Swiss police had been contacted and security measures had been taken to ensure the council meeting could go on "with calm and dignity".

A Reuters witness saw Swiss police guarding the team even though the meeting was held within the United Nations compound in Geneva. A police spokesman said he could not immediately comment.

Mike Smith, who led the commission of inquiry into Eritrea, said the threats were related to a demonstration against the inquiry on Monday, when 6,000 people from Eritrea and around Europe protested outside the U.N., organisers said.

"Accidentally or not, members of the commission came into contact with some of the demonstrators. And there was a bit of a discussion that got a little bit more than that," Smith said.

There was also "stuff on the blogosphere" aimed at his fellow commissioner Sheila Keetharuth, which he said was "not very pleasant".

Keetharuth said the threats were "specific" but declined to give details.

Smith said the government was able to influence Eritrean communities abroad and was "very active" in promoting its interests abroad, while witnesses were scared to give evidence even though they were living securely outside the country.

Eritrea's government systematically spies on individuals and entities inside and outside Eritrea, the inquiry's report said.

Harsh conditions in the country have been widely blamed for an exodus of around 5,000 Eritreans fleeing to Europe across the Mediterranean each month.

The U.N. inquiry, constrained by its terms of reference, stopped short of declaring whether Eritrea's government was committing crimes against humanity but recommended this be examined further, so a decision could be taken about whether to refer the case to the ICC.

Eritrea's neighbours Djibouti and Somalia are backing a Human Rights Council resolution to extend the team's mandate for a year to enable it to say if crimes against humanity were committed and to ensure "full accountability".

"The government must understand that the system that they have set up is simply unacceptable in the modern world," Smith said.

Eritrea has not cooperated with the investigators nor let them into the country. It has tried to discredit the methodology and motives of the report but has not shown any contrary evidence, he said.

Its ambassador Tesfamicael Gerahtu was upbraided by Ruecker for telling the council that the commission was "ignorant", that it had "a sinister political agenda" and that their report - based on 550 interviews and 160 written statements - was "a travesty of justice". (Editing by Raissa Kasolowsky/Hugh Lawson)