* Benchmark Bund yields lowest in nearly six weeks
* French equivalents lowest since early January
* Qatar rift, Comey testimony top political fears
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices)
LONDON, June 6 (Reuters) - Euro zone government bond yields hit multi-week lows on Tuesday as geopolitical tensions from the Middle East to the United States pointed to slower price growth.
A diplomatic rift between Qatar and several Arab states including Saudi Arabia has depressed oil prices as it could undermine efforts by OPEC to tighten the market.
Combined with doubts about the U.S. economy and President Donald Trump's ambitious spending plans, the oil slide is clouding the outlook for price growth globally.
In turn, this weak outlook is keeping demand high for bonds, even though the European Central Bank is expected on Thursday to take a more benign view of the economy and potentially close the door to further stimulus.
"There is a general risk aversion theme going on," said Mizuho's head of euro rates strategy, Peter Chatwell.
"The evolution of data in the U.S. has also justified the drop in global government bond yields, and is why investors in Europe feel comfortable at these levels."
Britain's election on Thursday, which some pollsters indicate could result in a hung parliament, is also spreading a cautious tone across markets in general.
German Bund yields fell to their lowest level in nearly six weeks at 0.25 percent. French equivalents fell below 0.70 percent for the first time since early January, narrowing the gap over German yields to 39 basis points - the tightest in almost a month.
An outperformance in French bonds came after polls suggested that Emmanuel Macron's party is set to win the biggest parliamentary majority for a French president since Charles de Gaulle's 1968 landslide.
Still, the fall in yields was widespread across euro zone markets. Spanish 10-year yields dropped as much as 5 bps to 1.52 percent, just above four-month lows, while Irish yields hit five-month lows at 0.73 percent.
Oil prices have shed around 8 percent over the last 10 days - a slide that has further eroded long-term inflation expectations in the euro zone.
The five-year, five-year forward rate has slid more than 20 bps since the start of the year to below 1.6 percent - well short of the ECB's near-2-percent inflation target.
Adding to the political tension, former FBI director James Comey is due to testify before the U.S. Congress on Thursday. He may discuss his conversations with U.S. President Donald Trump about an investigation into former National Security Advisor Mike Flynn, who was fired for failing to disclose conversations with Russian officials.
Investors see this as a distraction for Trump, who they are banking on to reflate the stuttering U.S. economy with ambitious spending plans.
In the U.S., long-dated U.S. Treasury yields fell to their lowest levels since November.
(Editing by Larry King)