By Tommy Stubbington and Josie Cox 

Stocks and bonds in Europe fell on Monday after Greece's voters set the country on a collision course with the rest of the eurozone, but it wasn't the heavy selloff predicted by many investors.

Greece's rejection of creditors' demands in Sunday's referendum appears to have pushed the country closer to an exit from the currency bloc. But with the Greek government expected to return to the negotiating table for further unpredictable talks, investors have shied away from big bets.

In the background, many fund managers assumed the European Central Bank would act swiftly to contain any fallout from the Greek crisis.

The result is a now familiar pattern: Markets are reacting with trepidation but not panic.

"We keep having these defining moments. We get past them and they don't seem to have defined very much," said Paul Lambert, head of currency at Insight Investment, which manages GBP397.2 billion ($618 billion).

"Until Greece's creditors close the door to a new deal, investors will be reluctant to draw any conclusions," he added.

The pan-European Stoxx Europe 600 was 1.2% lower early Monday afternoon. In the U.S., the S&P 500 fell 0.5% in early trade.

Italy and Spain--two of the countries seen as most at risk from the Greek crisis--were hardest hit, with losses concentrated in banking stocks.

Milan's FTSE MIB index fell 3.7% and Madrid's IBEX 35 lost 2.3%. Greece's stock markets were closed last week and won't reopen until Tuesday at the earliest, along with the country's banks.

The euro initially tumbled before rebounding slightly. It traded 0.7% lower against the dollar at $1.1032 Monday, slightly above the lowest level it hit last week.

Crucially, the reaction in bond markets was mild.

Bonds issued by highly indebted Southern European countries have in the past been vulnerable to fears that a Greek exit from the eurozone could foreshadow a wider breakup of the currency bloc.

Many had expected those fears to return after the Greek vote.

However, Spanish and Italian 10-year bond yields climbed by around 0.1 percentage point to 2.32% and 2.35% respectively, below their recent highs. Yields rise as prices fall.

German bonds, which are seen as a haven by investors, gained. Germany's 10-year yield was 0.05 percentage point lower at 0.75%.

"Given what has happened it seems a very muted move," said Daniel Loughney, a portfolio manager at AllianceBernstein, which manages $500 billion of assets. But Mr. Loughney doesn't want to make any negative bets on Italian or Spanish debt, given the potential for the ECB to beef up its asset-purchase program to prop up markets.

"I think these markets remain very vulnerable, but we don't want to fight the ECB in the near term," Mr. Loughney said.

The resignation of Greece's confrontational finance minister Yanis Varoufakis on Monday was also helping to soothe markets, he added.

In Asia, stocks in Hong Kong tumbled, while China's stabilized, as Beijing took unprecedented steps to stem a three-week selloff.

Some investors said that although the fallout seemed limited on Monday, it was too early to dismiss the risks.

"Just because we're not seeing some kind of Armageddon in markets doesn't mean that markets won't continue to be dragged lower," said David Stubbs, global market strategist at J.P. Morgan Asset Management, which manages $1.7 trillion.

He added that if the situation deteriorates and a disorderly Greek exit becomes likely, then investors will have to start "looking very carefully at deposit levels in Portuguese and Spanish banks."

In commodity markets, Brent crude oil was 2.1% lower on the day at $59.04 a barrel. Gold was flat at $1,164.20 a troy ounce.

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