* Fed, BOJ meetings this week see caution set in
* Dollar starts week on the back foot
* Crude oil drops after logging 3rd weekly rise
* European shares fall 0.7 percent, dropping for 3rd day
By Marc Jones
LONDON, April 25 (Reuters) - World stocks, the dollar and oil all saw modest falls on Monday as investors locked in some recent gains ahead of central bank meetings in the United States and Japan this week.
Asia and Europe both sank as Tokyo gave back 0.8 percent of the 4 percent it had made last week and 3 and 1.5 percent falls for miners and oil firms pushed the FTSEurofirst 300 down for a third straight day.
As well as signs the 3-month rally in stocks and commodities markets is cooling, a U.S. Federal Reserve rate decision on Wednesday and the Bank of Japan meeting on Thursday meant there was little incentive for traders to be bold.
Talk has been that Japan could push deeper into negative interest rate territory, while there is intense interest on where the Fed currently stands on another rate hike.
"Central banks are still the name of the game," said Nordea's chief strategist for developed markets, Jan von Gerich.
"There is a chance that the Fed could surprise with a bit of hawkishness on Wednesday. The dollar hasn't really strengthened and the S&P 500 is back near its all-time high, so they could certainly test the market."
The dollar index was trading 0.2 percent lower on the day at 94.963. Against the euro, it dipped to $1.1270, at the weaker end of a 10-cent range it has held for a year, while the yen rose to 111.24 after a walloping at the end of last week.
Britain's sterling, meanwhile, had hit its highest in over a month after a UK media blitz from President Barack Obama calling for Britain to stay in the European Union saw bookmakers lengthen the odds of a Brexit vote in June.
"If one of our best friends is in an organisation that enhances their influence and enhances their power and enhances their economy, then I want them to stay in it," Obama said.
The subdued start to the week for Europe's stock markets, was further compounded by an unexpected fall in German business morale data.
The Munich-based Ifo economic institute said its business climate index, which surveys around 7,000 firms, dipped to 106.6 in April compared to a forecast of a rise to 107.0.
One of IFO's top economist said the mood in the German economy was still good, however, albeit not euphoric.
BOJ MEETING
The jittery mood sent investors back into government bonds, having largely shunned them for the last couple of weeks.
Bund yields fell a fraction but remained above 0.2 percent having ended Friday with their biggest weekly rise since last December.