European shares sag after Trump ousts U.S. chief diplomat

* Dollar falls after Tillerson ouster

* STOXX 600 falls 1 pct

* Dividend hike sends E.ON up 3.9 pct

* Iliad (LSE: 0MGY.L - news) tumbles on disappointing fixed-line numbers (Releads, adds comments, context)

By Helen Reid and Julien Ponthus

LONDON, March 13 (Reuters) - European shares closed firmly in negative territory on Tuesday as the euro rose against a faltering dollar after U.S. President Donald Trump fired Secretary of State Rex Tillerson.

The pan-European STOXX 600 ended the session down 1 percent with Frankfurt's DAX and its German exporter constituents taking the worst hit, down 1.6 percent.

The euro zone currency, a rise in which typically hurts European blue-chip companies, climbed about 0.5 percent against the dollar on Tuesday.

"There is the Tillerson effect and there's the euro-dollar effect," said Oddo Securities trader Mikael Jacoby, noting that investors probably saw Tillerson's removal as a good reason to take some profits after six trading days of gains.

The departure of Gary Cohn as President Donald Trump's top economic adviser and worries about a possible global trade war had already sent jitters through global financial markets.

"What we are seeing here is that those people in the U.S. administration in the more moderate line of thinking are being ousted, so this adds to the concerns the more radical forces are gaining some ground," said Rabobank's head of macro strategy Elwin de Groot.

The utilities sector retreated 0.25 percent retreat, with losses limited by demand for German utilities RWE (IOB: 0FUZ.IL - news) and E.ON as they plan to divide up the assets of power firm Innogy.

E.ON got a further boost and posted the second best-performance of the STOXX 600, up 3.9 percent after it said it would raise its dividends for 2018 and 2019.

French telecoms company Iliad fell 9.9 percent after missing market forecasts due to losses related to its launch in Italy.

Iliad's rival Orange (LSE: 0OQV.L - news) , the dominant French telecoms company, returned to growth last year for the first time since 2009 after spending heavily to roll out high-speed broadband.

Struggling South African retailer Steinhoff saw its Germany-listed shares rise 2.1 percent after it cut its stake in KAP Industrial as it tried to plug a liquidity gap.

Veolia fell 2.4 percent, the top faller on France's CAC 40, after the Qatari government sold its 4.6 percent stake in the utility group.

A weaker full-year outlook sent chemicals group Wacker Chemie down 6.6 percent. The firm said sales would slow due to currency pressures.

Overall European company results have been encouraging. Investors said European earnings had further room to grow as they were still lagging those in the United States.

"The European market isn't pricing in quite as much as the U.S. is, and it's in a more favourable part of the business cycle," said Rothschild's Gardiner.

"We are aware that it's a pretty crowded story, but we still think it's very attractive."

(Reporting by Helen Reid and Julien Ponthus Editing by Catherine Evans)