Interest rate worries that have boiled up again have the European stock markets firmly in their grip.

Dax and EuroStoxx50 were each down 0.3 percent on Tuesday at 14,401 and 3,946 points.

After consistently better than expected US economic figures, the stock markets are in a difficult situation, said portfolio manager Thomas Altmann from the investment advisor QC Partners.

"Because the continued thriving US economy could push the Fed to hike rates longer and push the end point higher."

Surprisingly strong growth in the US service sector recently exacerbated investors' concerns about interest rates.

Earlier on Friday, stronger-than-expected US jobs data dampened speculation that the Federal Reserve might slow the pace and intensity of its rate hikes given recent signs of slowing inflation.

The dollar index, which shows the exchange rate against major currencies, was stable at 105.20 points on Tuesday after interest rate speculation boosted the US currency on Monday.

According to chief economist Philip Lane, the ECB will also have to raise interest rates several times, even if inflation is likely to have almost peaked.

In the executive floor of the European Central Bank (ECB), voices have recently increased that, after two large interest rate hikes in a row, now expect a less aggressive pace.

Oil price turns negative again

On the crude oil market, oil prices have given back initial gains again after the recent decline.

The price of Brent crude oil and US oil WTI fell by around one percent to $ 81.75 and $ 76.08 per barrel (159 liters).

Investors continued to weigh the impact of Western sanctions on Russian crude.

The price cap on Russian oil transported by sea has been in effect since the beginning of the week, at $60 per barrel.

Russia will change its logistics chains in response to the price cap, Deputy Prime Minister Alexander Novak announced, according to Russian news agencies.

After crude oil prices had already fallen by almost 3.5 percent overnight, the oil and gas sector also came under pressure.

The industry giants Shell, BP and TotalEnergies lost between one and 1.7 percent.

Meanwhile, Fresenius Medical Care (FMC) led the list of losers in the German share index.

After just over two months, Carla Kriwet will be replaced by CFO Helen Giza at the helm of the dialysis group.

The company called "strategic differences" on Tuesday night as the reason for the abrupt change in the executive chair.

"There's a lot of trouble here," said one trader.

FMC shares are down more than four percent, having lost more than half their value since April.

On the other hand, the new composition of the index, which Deutsche Börse announced on Monday evening, had little effect on prices.

A good two months after the IPO, the Stuttgart-based sports car manufacturer Porsche AG is already being included in the leading index Dax, replacing the shares of the sporting goods manufacturer Puma on December 19.

The stocks of Porsche AG were up 1.5 percent at the top, Puma shares also increased by up to almost two percent.