Turkey sent warplanes and troops into northeastern Syria on Wednesday in a military operation aimed at flushing out an American-backed militia, Turkish and Syrian officials said.

The Turkish attack came amid a flurry of confusing policy statements from the White House, which on Sunday acquiesced to the operation, agreeing to move American forces out of the way, but on Wednesday, hours after it began, condemned it.

“The United States does not endorse this attack and has made it clear to Turkey that this operation is a bad idea,” President Trump said in a statement on Wednesday.

Turkish fighter jets streaked through the sky over Syrian towns, while explosions from artillery shells boomed, causing traffic jams of terrified civilians fleeing south in trucks piled high with their possessions and children.

After about six hours of airstrikes, Turkish troops and their Syrian rebel allies crossed the border late Wednesday, the Turkish Defense Ministry, beginning a ground offensive.

At least seven people were killed in Turkish attacks on Wednesday, according to the Rojava Information Center, an activist group in northeastern Syria. The Syrian Observatory for Human Rights, a conflict monitor based in Britain, put the toll at eight.

Turkey’s long-planned move to root out United States-allied Kurdish forces in northeastern Syria has accelerated rapidly since Mr. Trump gave the operation a green light in a call with President Recep Tayyip Erdogan of Turkey on Sunday