* Phone intercept hears rebel talking of "sea" of bodies
* Ukraine official says rebels "will not dance on corpses"
* Ukraine wants Russian officers punished (Adds background)
By Natalia Zinets and Richard Balmforth
KIEV, July 17 (Reuters) - Ukraine's state security chief accused two Russian military intelligence officers of involvement with pro-Russian rebels in the downing of a Malaysian airliner on Thursday, releasing chilling testimony of what he called an "inhuman crime."
SBU chief Valentyn Nalivaychenko based his allegation on intercepted telephone conversations between the two officers and pro-Russian fighters, one of whom referred to seeing "a sea of women and children" in the wreckage of the Malaysia Airlines Boeing 777.
"We will do everything for the Russian military who carried out this crime to be punished," Nalivaychenko told journalists, who were shown video and audio transcripts of the recordings. "The terrorists will not go on dancing on corpses."
In a recording played to journalists of a conversation said to have taken place at 4.33 p.m. Kiev time (13:33 GMT), a rebel fighter going by the nom de guerre of 'Major' is heard telling another comrade called 'Grek' that a group of fighters had brought the airliner down.
"The plane broke up in the air, near the Petropavlovskaya mines. The first (casualty) has been found. It was a woman. A civilian," he says.
At 5.42 p.m. 'Major' acknowledges the plane was civilian: "Hell. It's almost 100 percent certain that it's a civilian plane."
Asked if there were many people on board, he replies in the affirmative with a swear-word, adding: "The bits (of the plane) were falling down in the streets ... There were the bits of couches, chairs, bodies."
Asked if any weapons were found on board, 'Major' says: "No - Civilian things, medical things, towels, toilet paper."
He says ID documents of an Indonesian student had been found.
In another recording of an intercept, played to journalists, a Russian (military intelligence officer) called Igor Bezler is heard reporting on the downing to his superior in Russian military intelligence, Colonel Vasily Geranin.
"A plane has just been shot down. It was the 'Mine-laying' group ... They've gone to search and photograph the plane. It is smoking," Bezler tells Gernanin at 4.40 p.m.
Asked 'How long ago?' he replies: 'About 30 minutes ago.'
In a third conversation, a rebel fighter says: "It turned out to be a passenger plane. It fell in Hrabove area. There's a sea of women and children ..."
He adds: "But what was it (the Malaysian airlines flight) doing over Ukraine?"
The man he is talking to replies: "That means they've called up spies. No way to flights. This is war"
"Okay, understood," he replies.
"They discuss Russian saboteurs bringing down a passenger plane. They discuss the number of victims. We have fixed this conversation as taking place at 4.20. Now you know who carried out this inhuman crime against humanity," Nalivaychenko said.
"We will open up to all possible channels, the means of this crime being objectively investigated, and the officers of the Russian Federation who carried out this crime being punished." (Editing by Andre Grenon)