* Europe shares fall, led by bank shares; Athens market still shut
* Wall Street drops less than some feared; IMF offers reassurance
* Oil sinks on worries over Greece, China and Iran (Updates with close of U.S. markets; adds detail on Greek banks)
By Noel Randewich
SAN FRANCISCO, July 6 (Reuters) - Equity markets around the world fell on Monday and U.S. oil prices tumbled 7 percent after Greece overwhelmingly voted against conditions for a rescue package and following unprecedented measures in China to staunch recent massive losses in its stock markets.
Wall Street shares fell less than some had feared. The International Monetary Fund reassured investors by saying it was ready to help Greece if asked to do so. European shares fell around 2 percent, a relatively muted reaction to the Greek vote.
Beijing introduced emergency measures over the weekend following a 30 percent slide in its stock market since mid-June, raising investors' concerns about the stability of the world's second-biggest economy.
Wall Street investors took heart after Greece's outspoken finance minister, Yanis Varoufakis, stepped down and Prime Minister Alexis Tsipras said his government was ready to return to negotiations with creditors in a bid to open shuttered banks.
"After the initial knee-jerk reaction, the majority opinion is that there is still a possibility of some sort of a deal that keeps Greece in the euro zone," said Mark Luschini, chief investment strategist at Janney Montgomery Scott in Philadelphia.
The Dow Jones industrial average fell 46.53 points, or 0.26 percent, to end at 17,683.58. The S&P 500 lost 8.02 points, or 0.39 percent, to 2,068.76, and the Nasdaq Composite dropped 17.27 points, or 0.34 percent, to 4,991.94.
Tsipras promised German Chancellor Angela Merkel that Greece would bring a proposal for a cash-for-reforms deal to an emergency summit of euro zone leaders on Tuesday after the surprisingly strong "No" vote in Greece's referendum Sunday.
Raising the stakes on the Greek leader, the European Central Bank decided to keep a tight grip on funding to Greek banks, which have been closed for more than a week to avoid a massive outflow of money that could lead to their collapse.
U.S. oil prices fell the most in three months after Greece's rejection of the debt bailout terms and after China's measures to support its stock markets.
Also taking a toll on the energy market were talks between Iran and world powers to meet a July 7 deadline on a nuclear deal. That deal could release more oil into already oversupplied markets if sanctions on Iran are eased.
Benchmark Brent crude declined 5.8 percent, down $3.51 a barrel at $56.82. U.S. light crude was 7.17 percent lower at $52.86.
"Uncertainty over Greece is bearish for oil," said Olivier Jakob, senior energy analyst at Petromatrix in Zug, Switzerland. "It adds an extra negative factor on top of the turmoil in Chinese financial markets, the recent rise in U.S. drilling rigs and a potential increase in Iranian oil supply."
MSCI's all-country equities world index lost 1.01 percent, while its emerging markets index dropped 2.13 percent.
The euro zone blue-chip Euro STOXX 50 index fell 2.22 percent. The pan-European FTSEurofirst 300 index was down 1.17 percent. The Athens stock market remained shut, but U.S.-listed Greek shares slid. National Bank of Greece's U.S. shares closed down 12 percent in New York while the exchange-traded fund Global X FTSE Greece 20 ETF fell 7.5 percent.
The euro was 0.54 percent weaker against the dollar, at $1.1053. The dollar index, a gauge of the greenback against six major currencies, edged up 0.16 percent after earlier hitting its highest point in a month.
Chinese stocks market climbed, going against the broader tide of declines in world markets. The CSI300 index of the largest listed companies in Shanghai and Shenzhen closed up 2.9 percent, while the Shanghai Composite Index gained 2.4 percent after brokerages and fund managers vowed to buy massive amounts of stocks, helped by China's state-backed margin finance company.
The rapid decline of China's previously booming stock market had become a major headache for China's top leaders, who were already struggling to avert a sharper economic slowdown.
Benchmark U.S. Treasury yields hovered near their lowest levels in over two weeks as safe-haven demand boosted bond prices. Yields on 10-year Treasuries hit 2.274 percent, their lowest level in over two weeks, while long-dated yields hit their lowest level in nearly one week at 3.088 percent. (Additional reporting by Hideyuki Sano in Tokyo and Patrick Graham, by Nigel Stephenson, Lionel Laurent and Alistair Smout in London; Editing by Bernadette Baum and Leslie Adler)