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PRECIOUS-Gold set for 5th week of gains, palladium hits record

* Automotive sector demand, tight supplies boost palladium

* Silver heading for first weekly drop in 5 weeks

* Platinum hits four-month high, tests $1,000

* Palladium hits record high of $1,117.50

(New throughout, updates prices, market activity and comments, adds palladium record; adds second byline and NEW YORK dateline) NEW YORK/LONDON, Jan 12 (Reuters) - Gold hit a four-month high on Friday and was on track for a fifth straight weekly gain as the U.S. dollar fell against the euro on an agreement for a political coalition in Germany. Palladium hit a record high in a continued rally fueled by tight supplies and increased demand in the automotive industry for autocatalysts in gasoline-burning vehicles.

Spot gold was up 1.2 percent at $1,338.39 an ounce by

2:19 p.m. EST (1919 GMT). The session high of $1,339.31 was its highest since September. Bullion is up 1.4 percent this week and set for its longest run of weekly gains since April.

U.S. gold futures for February delivery settled up

$12.40, or 0.9 percent, at $1,334.90 per ounce.

Palladium rose 3.4 percent to $1,120.24 per ounce and

was up 2.8 percent for the week. During the session it hit a record high of $1,126.30. Gold prices extended their rally after U.S. President Donald Trump said he would waive nuclear sanctions against Iran for the last time to give Washington and its European allies a chance to fix the "terrible flaws" of the 2015 nuclear deal. "This is a last chance," Trump said in a statement, which fed investor worries and boosted safe-haven demand for gold. "Certainly, Trump making that announcement helped, and it's been a risk-on move today," said Dan Hussey, senior market strategist at RJO Futures in Chicago.

The dollar index , fell against a basket of currencies

to its lowest since Sept. 8. The euro jumped to a three-year high after party sources said German Chancellor Angela Merkel's conservatives and the Social Democrats (SPD) had agreed a blueprint for formal coalition negotiations. "The agreement is one of the first movements in a long time that people say is EU-positive. Hence the strength in the euro and gold, as well," Hussey added. A stronger euro makes dollar-priced bullion cheaper for European investors. The U.S. dollar saw some pressure from falling producer prices in the United States in December, as underlying U.S. consumer prices recorded their largest increase in 11 months.

Both U.S. data reports tempered inflation worries. Palladium has seen a sustained rally from high demand in the auto industry and a supply deficit, a New York-based trader said. "It's spiking, but platinum is starting to follow it higher," he added.

Platinum rose 1.1 percent at $994.90 an ounce after

touching its highest since Sept. 11 at $998.50, on track for a fifth straight weekly gain. Platinum is up 2.6 percent so far this week.

Spot silver rose 1.4 percent at $17.20 an ounce but

was still heading for its first weekly loss in five weeks, down 0.1 percent for the week.

(Additional reporting by Nallur Sethuraman in Bengaluru; Editing by David Gregorio and David Goodman)