By Josie Cox and Tommy Stubbington 

Frustration at an apparent lack of progress in last ditch-efforts to keep Greece in the eurozone jolted markets Tuesday, with stocks falling sharply for a second day and safe-harbor assets rallying.

Markets in Europe had made a steady start, but the mood soured. During Tuesday's finance ministers' meeting, Greek finance chief Euclid Tsakalotos only read out proposals the government already presented last week, but promised that a new plan would be sent to creditors Wednesday, three European officials said.

"There was hope of some kind of breakthrough today. That hope is subsiding now," said Guy Foster, head of portfolio strategy at wealth manager Brewin Dolphin.

The Stoxx Europe 600 fell 1.6%, deepening Monday's declines. In the U.S., the S&P 500 was 0.8% down as European markets closed.

"I'm absolutely amazed by the Greek government not proposing anything new at the Eurogroup meeting," said Wouter Sturkenboom, senior investment strategist at Russell Investments, which has around $272 billion in assets under management.

"I think the market is really shocked by this lack of any new attempts to negotiate," he said.

The euro fell to a five-week low against the U.S. dollar and was recently down 1.0% at $1.0955.

"There is a slow realization that we will have to consider the implications of Greece exiting the monetary union. Today we're one day closer to that potentially being the case," said Hamish Pepper, a currencies strategist at Barclays.

"People are choosing the U.S. dollar as their preferred safe haven to go to in this time of uncertainty over Greece," he said.

Bond markets showed signs of stress. Prices of German debt, seen as a haven by investors, climbed. The yield on Germany's 10-year benchmark bond fell 0.14 of a percentage point to 0.63%, also a five-week low. Yields fall as bond prices rise.

Ahead of a eurozone summit, the currency bloc's finance ministers said it was up to Greece to present credible new proposals after the country's voters rejected austerity measures demanded by creditors.

Without a fresh inflow of funds, Athens will be unable to make a EUR3.5 billion ($3.9 billion) bond repayment to the European Central Bank on July 20.

The head of Greece's banking association said banks would remain closed through Wednesday. They were closed all of last week, as was the country's main stock exchange. The Athens bourse remained closed Tuesday, and it will be on Wednesday as well.

In commodity markets, Brent crude was 0.7% lower at $56.13 a barrel. On Monday, oil prices recorded their biggest single-day declines in more than three months, as gyrations in Chinese stocks and the prospect of more crude from the U.S. and Iran revived worries about the global supply glut.

Gold was 1.9% lower on the day at $1,150.70 a troy ounce.

Write to Tommy Stubbington at tommy.stubbington@wsj.com and Josie Cox at josie.cox@wsj.com