* One of world's largest LNG exporters stops Red Sea route

* U.S., Britain target Houthis in Red Sea spillover from Gaza war

* 'Let's wait and see,' says UK of more potential strikes

* U.S. says it shoots down cruise missile fired from Yemen

DOHA/WASHINGTON, Jan 15 (Reuters) - Qatar's state energy company, one of the world's biggest liquefied natural gas exporters, has paused sending tankers through the Red Sea after U.S.-led strikes against Houthi militants in Yemen targeting the crucial trade route.

Attacks on ships by the Houthis, who say they are acting in solidarity with Palestinians, have disrupted global commerce and alarmed major Western powers in a spillover from Israel's more than three-month war with Hamas militants in Gaza.

In the latest shift by a major firm, state-owned QatarEnergy has held at least four LNG tankers back from the Red Sea, a senior source said, adding that production continues.

That followed dozens of U.S. and British strikes on the Houthis in Yemen. They have been at war with a Saudi-led coalition for years, but have also turned their sights on the sea next to them as a way to put pressure on Israel.

The U.S. military said late on Sunday that its fighter aircraft shot down an anti-ship cruise missile fired by the militants toward a U.S. destroyer. No injuries or damage were reported, according to a military statement on X.

On Monday, carmaker Suzuki said production would halt at its Esztergom plant in Hungary from Jan. 15-21 as the Red Sea attacks had delayed the arrival of Japanese-made engines.

The Houthis have vowed to keep targeting Israel-linked ships and to give a firm response to the attacks on them.

U.S. ally Britain said it had no desire to be involved in a Red Sea conflict but was committed to protecting the right of free navigation. "Let's wait and see what happens," said Defence Secretary Grant Shapps of potential further strikes.

'PAUSE FOR SECURITY ADVICE'

LSEG shiptracking data showed that Qatar's Al Ghariya, Al Huwaila and Al Nuaman vessels had loaded LNG at Ras Laffan and were heading to the Suez Canal before stopping off Oman on Jan. 14. The Al Rekayyat, which was sailing back to Qatar, stopped along its route on Jan. 13 in the Red Sea.

"It is a pause to get security advice, if passing Red Sea remains unsafe we will go via the Cape," the source told Reuters on Monday about QatarEnergy.

The longer route round Africa's Cape of Good Hope can add about 9 days to the normally 18-day trip to Europe.

The Qatari government and QatarEnergy did not immediately respond to requests for comment.

The Red Sea is linked to the Mediterranean by the Suez Canal, creating the shortest shipping route between Europe and Asia, and is connected to the Gulf of Aden by the Bab-al-Mandab strait between Yemen and Djibouti.

About 12% of world shipping traffic transits the canal.

Front month European benchmark gas prices on the Dutch TTF hub were down 1.20 euros at 30.40 euros per megawatt hour (MWh) in early trade on Monday, LSEG data showed.

Asia spot LNG prices fell to a seven-month low of $10.10 per million British thermal units (mmBtu) on Friday, supported by healthy storage levels in Europe and northeast Asia.

Oil prices edged lower on Monday as oil supplies remain unaffected, despite escalating tensions in the Middle East, after rising 2% last week on potential disruptions emanating from the conflict.

(Reporting by Reporting by Maha El Dahan in Davos, Emily Chow in Singapore, Andrew Mills in Doha, Sachin Ravikumar in London, Chandni Shah in Bengaluru; Writing by Andrew Cawthorne; Editing by Catherine Evans)