* Virus surges in U.S. south and west

* California, Texas, Florida re-imposing restrictions on business

* Risk-currency rally stalled as dollar holds ground

* Graphic: World FX rates in 2020 https://tmsnrt.rs/2RBWI5E

By Tom Westbrook

SINGAPORE, June 29 (Reuters) - A firm dollar kept riskier currencies under pressure on Monday, as a surge in coronavirus cases and the re-imposition of curbs to stop its spread had investors worried that a global economic recovery could be derailed even before it had taken root.

California ordered some bars to close on Sunday, following similar moves in Texas and Florida, as cases nationwide soar to record levels each day. Washington state and the city of San Francisco have paused re-opening plans.

That allowed the greenback to hang on to gains ground out last week, and had riskier currencies such as the trade-exposed Australian and New Zealand dollars parked toward the bottom of ranges they have held for several weeks.

The Aussie was last steady at $0.6872 and the kiwi at $0.6420 - though both are set for monthly gains of roughly 3% as the rising risks to the global recovery have stalled rather than reversed their steep rally.

Against a basket of currencies the dollar was steady not far below a four-week peak on Monday at 97.466. The safe-haven Japanese yen also held at 108.18 per dollar.

"A double-dip U.S. recession is possible if widespread restrictions are re-imposed, leading to a surge in the dollar," said Commonwealth Bank of Australia FX analyst Joe Capurso.

"Lockdowns are the key indicator to watch."

The jump in U.S. cases has been most pronounced in a handful of Southern and Western states that reopened earlier and more aggressively, serving as a warning to the potentially illusory nature of perceived progress in controlling the virus.

New restrictions on movement have also been imposed in parts of Beijing and Lisbon and in two municipalities in western Germany. Argentina extended and tightened a lockdown around Buenos Aires following a sharp rise in cases.

Globally half a million people have died from COVID-19, about a quarter them in the United States.

Elsewhere sterling nursed losses and sat at $1.2341, just a fraction above a one-month low it hit on Friday amid fresh doubts over whether Britain can settle a post-Brexit trade pact with the European Union.

The euro is set to wrap up its best two months against the dollar in a year and a half, as hopes for a united EU response to the virus and a swift regional recovery propel the single currency ahead about 2.5% since the beginning of May.