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Tillerson ouster gives fresh boost to safe-haven euro zone bonds

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr

LONDON, March 13 (Reuters) - Euro zone government bond yields fell on Tuesday following news that U.S. President Donald Trump has ousted U.S. Secretary of State Rex Tillerson, injecting a fresh dose of volatility into world markets.

Data showing that U.S. inflation slowed in February also reassured investors, putting downward pressure on bond yields on both sides of the Atlantic.

"Treasuries reversed direction on the fear that Tillerson's removal will give the nationalists greater power within the White House over the globalists," said Investec economist Philip Shaw.

Trump said he had replaced Tillerson with Central Intelligence Agency Director Mike Pompeo, and had tapped Gina Haspel to lead the CIA.

The U.S. 10-year Treasury yield fell as much as 3 basis points on the Tillerson news and was last trading at around 2.85 percent, also held down by news of slowing inflation.

In Europe, bond yields fell 1-3 basis across the board.

Germany's 10-year government bond yield fell 2 bps to around 0.61 percent, its lowest level in just over a week.

Europe's STOXX 600 fell to a session low on the news and were last down 0.2 percent. The pan-European banks index also tumbled to the day's low, down 0.2 percent.

The dollar, meanwhile, extended its fall. It had already been weak across other G10 currencies after U.S. inflation data came in as per forecasts but it skidded further as the sell-off accelerated.

Against a basket of currencies, the dollar fell 0.2 percent , while the euro gained 0.3 percent to $1.2369.

Earlier, a decent demand at Italian bond auctions helped underpin sentiment in euro zone bond markets.

The bond sales come against a backdrop of uncertainty following an inconclusive March 4 election, which investors appear to be largely shrugging off for now.

Elsewhere, Slovakia's 10-year bond yield rose as much as five basis points SK10YT=RR and the cost of insuring exposure to its debt hit the highest in almost three months as the government inched towards collapse.

They continued to underpeform euro zone peers after news of Tillerson's departure.

Slovakia's three ruling coalition parties were holding talks on Tuesday, a government spokeswoman said, after a junior member called for an early election following mass protests against corruption and the murder of a journalist last month.

(Additional reporting by Helen Reid and Tommy Wilkes)