* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh (Recasts, adds analyst quote)
NEW YORK, Oct 22 (Reuters) - The U.S. dollar rose on Monday as the British pound fell on news that Brexit negotiations with the European Union over Northern Ireland remain in flux and as the euro continued its slide on political uncertainty over Italy's budget.
Prime Minister Theresa May on Monday said most of Britain's deal to exit the EU has been agreed on but repeated her opposition to a EU proposal regarding the Irish border, according to excerpts from her statement to Parliament. Sterling was down 0.73 percent in the North American session at $1.297 , continuing a slide that began at the start of last week.
With just over five months until Britain is scheduled to exit the EU, talks have stalled over a disagreement on the so-called Northern Irish "backstop," an insurance policy to ensure there will be no return to a hard border on the island of Ireland if a future trading relationship is not agreed upon in time.
The dollar index, which measures the greenback against a basket of six other currencies, was up 0.36 percent on the day, last at 96.003.
"The dollar moved on the back of sterling and the euro," said Shahab Jalinoos, global head of foreign exchange strategy at Credit Suisse.
The euro failed to hold early-session gains as investors focused on the likelihood of further political uncertainty in Europe over Italy's spending plans, despite a large drop in Italian government borrowing costs.
Rating agency Moody's downgraded Italy's credit rating on Friday but unexpectedly kept the outlook at stable.
That, along with more conciliatory comments from Italian officials that they were ready to sit down with EU officials and did not intend to expand the deficit beyond 2019, boosted demand for Italian debt after a weeks-long sell-off.
But the euro, its fortunes increasingly linked this year to Italian bond prices, failed to hold early gains and dropped 0.71 percent from a session high of $1.1550. It was last at $1.147 .
"We have more conciliatory tones from both sides, but it is still clear that this dispute is not over yet," Commerzbank analyst Thu Lan Nguyen said.
The single currency also weakened against the Swiss franc by 0.40 percent and was last at 1.423. But it remained stronger against the pound, up 0.27 percent, last at 88.37 pence .
Equity markets were mostly positive as hopes that China's tax cuts next year could be worth more than 1 percent of gross domestic product sparked a rally in Asian shares that fed across to Europe and the United States. (Reporting by Kate Duguid and Tommy Wilkes; Editing by Dan Grebler and Tom Brown)