What began as a weak day in the stock markets ended in the worst rout in more than two years, as investors dumped stocks amid anxiety that both Europe and the United States were failing to fix deepening economic problems.

With a steep decline of around 5 percent in the United States on Thursday, stocks have now fallen nearly 11 percent in two weeks. Markets have been plunging as investors sought safer havens for their money — including Treasury bonds, which some had been avoiding during the debate over extending the nation’s debt ceiling.

Sparking the drop was an unsuccessful effort by the European Central Bank to reassure the markets, which instead ended up spooking investors. The bank intervened with a show of support to buy bonds…