(Reuters) - Israel has signaled it would accept, as a first priority, world powers focusing on persuading Iran to stop higher-level uranium enrichment when they resume stalled nuclear negotiations this week with Tehran.

Israel, which has threatened last-resort attacks on its arch-foe´s nuclear facilities if diplomacy fails, demanded last month that any negotiated resolution should end all uranium enrichment, high and low level, and remove all fuel already stockpiled by Iran.

But Western diplomats have said the six powers - the United States, Britain, France, Russia, China and Germany - that are due to open new talks with Iran on Friday would first tackle its uranium refinement to a fissile concentration of 20 percent rather than its more abundant 3.5 percent-pure fuel. The two sides have not yet agreed where the talks will take place.

The 20 percent enriched uranium would be far easier to enrich to bomb- grade 90 percent purity, though Iran denies having such designs, saying it is only seeking electrical energy and medical isotopes.

"We told our American friends, as well as the Europeans, that we would have expected the threshold for successful negotiations to be clear, namely that the P5+1 will demand clearly that - no more enrichment to 20 percent," Barak said in an interview with CNN´s Fareed Zakaria GPS to be aired on Sunday.

Iran´s stocks of 20 percent-pure uranium should be removed "to a neighboring, trusted country", Barak said, according to an advance transcript of the interview.

Iran says it has a sovereign right to peaceful nuclear technology and has repeatedly rejected U.N. resolutions calling for a suspension of all uranium enrichment.

But it has at times appeared more flexible regarding 20 percent enrichment, which it began in early 2010, and some experts say that initially getting Iran to stop this higher-grade work could open a way to ease the deadlock.

Asked about Barak´s comments to CNN, another Israeli official confirmed that the Netanyahu government was focusing lobbying efforts on Iran´s 20-percent pure uranium but said the long-term goal remained the ending all of its enrichment work.

"The understanding that has emerged in our contacts with the powers is that there should be a staggered approach," the official told Reuters on condition of anonymity.

COUNTDOWN ON ISRAELI DECISION

Western diplomats have similarly stressed that an initial focus on 20 percent enrichment should not be seen as "legitimizing" lower-level work as the U.N. Security Council has demanded a full suspension.

Iran has enough 3.5 and 20 percent-enriched uranium for around four bombs if refined further, Western experts say.

Barak´s remarks dovetailed with what the New York Times said on Saturday would be submitted to Iran by the United States and other Western nations in the upcoming talks.

According to the report, the world powers, which have ramped up sanctions against Iran, also plan to press it to close and ultimately dismantle a recently completed enrichment bunker in a mountain near Qom - another demand leveled by the Israelis.

Israel´s Yedioth Ahronoth newspaper said Prime Minister Benjamin Netanyahu presented U.S. President Barack Obama last month with propositions for an Iran deal that included allowing limited operations at its main enrichment facility at Natanz.

Netanyahu´s office had no comment on the Yedioth report.

Many analysts believe it may be unrealistic to demand that Iran suspend all enrichment as its leaders have invested so much national and personal prestige in the project.

In return for allowing limited, low-level enrichment, those analysts argue, Iran would need to accept much more intrusive U.N. inspections to make sure there is no military diversion.

Widely assumed to have the Middle East´s only atomic arsenal, Israel considers a nuclear-armed Iran would be a mortal threat.

"We don´t have to make a decision next week, and we cannot wait years, though," Barak said in the CNN interview when asked about the prospect of an Israeli pre-emptive attack. "We don´t have any decision about what to do or a date for (a) decision."

He dismissed speculation that Israel might settle for a Cold War- style nuclear deterrence with the Iranians if they get the bomb.

"No mutually assured destruction kind of situation ... will serve as a modifier or stabilizer in this case, because we are not continents, and Israel is not either the United States or the Soviet Union," Barak said.

(This has been refiled to clarify in first paragraph talks due this week) (Writing by Dan Williams; Editing by Will Waterman) (© Thomson Reuters 2012. 04/08/12)