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UPDATE 3-Spain bond yields hit three-month highs as Catalan tensions persist

* Euro zone bond yields broadly higher

* Strong U.S. economic data pushes up dollar

* Weaker euro keeps ECB policy outlook in focus

* Spain in spotlight as Catalonia tensions simmer

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Recasts to focus on Spain)

LONDON, Oct 3 (Reuters) - Spain's 10-year borrowing costs hit their highest level in nearly three months as tensions between Madrid and the Catalonia region spilled on to the streets on Tuesday after the weekend's illegal independence referendum.

Metro stations were closed in Barcelona, pickets blocked roads and state workers walked out in protests across Spain's wealthiest region over a Spanish police crackdown on Sunday's referendum.

Having already risen on Monday after the vote, the gap between Spanish and German 10-year borrowing costs was at its widest level since early June at 126 basis points.

"We don't believe the Catalan debacle is a flash in the pan, we think it will pose some threat to Spain's credit risk profile in the long term," said Rabobank strategist Richard McGuire.

"At an extreme, it does raise questions about this government's longevity," he said.

On Friday, ratings agency S&P Global maintained Spain's rating at BBB+ but said the positive outlook could be revised lower if the tensions between Madrid and Catalonia escalated and started weighing on business confidence and investment.

Even on a day when most euro zone bond yields rose, Spain was a clear underperformer, its 10-year yields jumping 5 basis points to 1.74 percent, its highest since July 10.

The cost of insuring exposure to Spanish sovereign debt rose on Tuesday to a near five-month high.

Data from IHS Markit showed five-year credit default swaps for Spain rose 1 basis point from Monday's close to 70 bps, the highest level since June 8 and up 16 bps from a trough of 54 bps on Sept. 19.

But some were sanguine on the issue.

"We don't think tail risks from Catalonia will continue because this is a Spanish issue not a euro zone existential issue," said Peter Chatwell, head of euro rates strategy at Mizuho.

Most other euro zone bond yields edged higher 1-2 bps on the day as strong U.S. data reinforced expectations of another interest rate rise this year by the Federal Reserve.

The U.S. Institute for Supply Management index, released on Monday, rose to 60.8 in September, from 58.8 in August, exceeding analyst expectations.

The overall mood across government bond markets was bearish as investors took their cue from upbeat data to sell fixed income and buy risk assets such as stocks.

"People are still watching what the Fed is doing and in Europe, how the ECB will act," said Benjamin Schroeder, senior rates strategist at ING.

A public holiday in Germany, however, made for subdued trade.

(Reporting by Dhara Ranasinghe; Editing by Catherine Evans)