BRUSSELS — The United States and its European allies on Thursday commemorated the 75th anniversary of D-Day, which freed the Continent from tyranny. But at the same time, the two sides are squabbling bitterly over the future and funding of European defense.

Washington has been pressing the European Union to spend more and do more for its own defense for well over a decade, with President Trump just the latest and loudest to do so.

Now that the European Union is actually responding, with a defense fund and a project for military cooperation and development, the United States is criticizing how it’s being done and complaining that the moves could harm trans-Atlantic cooperation and prevent American companies from competing for potentially lucrative contracts.

If anything, the spat is another reminder of the sour state of relations between the Trump administration and the European bloc and of the divisions on issues such as trade, climate change and Iran. The fact that a European plan to increase military spending — acceding to a demand from Mr. Trump — has degenerated into acrimony only emphasizes the split.