* Dollar index just shy of July 20 high
* Australian dollar slips as central bank holds rates (Updates prices, market activity; adds analyst's comments)
NEW YORK, Nov 7 (Reuters) - The dollar edged higher against a basket of currencies on Tuesday, as investors renewed their focus on diverging monetary policy between the United States and the euro zone.
The dollar index, which tracks the greenback against six major currencies, was up 0.17 percent at 94.921. The index is just shy of the three-month high of 95.150 hit late last month.
The euro was 0.2 percent lower at $1.1586 against the dollar. Its session low was $1.1555, its lowest since July 20.
"There is a renewed focus on the diverging policy outlook between the Fed and most other major central banks," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.
"The idea that the U.S. is going to normalize policy more quickly than other major central banks was largely put on the back burner for most of this year," he said.
"That story has once again come back into the spotlight as a result of the ECB meeting most recently," he said.
Late last month, the European Central Bank prolonged its bond purchases well into 2018, diminishing chances it would raise interest rates next year. Meanwhile, investors expect the U.S. Federal Reserve to raise interest rates next month followed by roughly two more hikes next year.
With this week being light on economic data, moves in the currency markets were muted as traders awaited next week's data on inflation and retail sales to provide direction, Alfonso Esparza, senior currency analyst at Oanda in Toronto, said.
"We haven't seen a lot of volume go through our platform today," he said.
Esiner said the dollar drew support from "cautious optimism" that lawmakers in Washington were making progress toward an eventual deal on taxes.
Republican lawmakers on Monday began revising their proposed overhaul of the U.S. tax code, as Democrats pointed to the loss of popular deductions as proof the legislation was an assault on the middle class.
Meanwhile, worries over the health of the economy as Britain prepares to leave the European Union kept sterling on a weak footing. The British pound was down 0.05 percent against the greenback.
Australia's central bank on Tuesday left its cash rate at a record-low 1.5 percent, and it looked likely to remain sidelined for months, with inflation low and debt-laden consumers cautious.
The Australian dollar slipped 0.61 percent to $0.7643 against the greenback. (Reporting by Saqib Iqbal Ahmed; Editing by David Gregorio and Susan Thomas)