* Dollar extends gains against yen, euro
* European shares open higher after rises in New York, Tokyo
* Gold extends losses
* Oil higher on kidnapping of Libyan PM
By Marc Jones
LONDON, Oct 10 (Reuters) - Shares and the dollar rallied on Thursday as the first signs of progress towards ending the budget and debt limit deadlock in Washington helped dial down fears of a calamitous U.S. default.
House Republican leaders will visit the White House later as efforts intensify to break the impasse that has left parts of the U.S. government shuttered for more than a week.
The dollar strengthened and was near a three-week high against most major currencies by the middle of the European session as recent U.S. lending market tensions also relaxed.
European stocks were strong too, up more than one percent and on course for their best day in exactly a month after closing on Wednesday at their lowest since Sept. 5. Wall Street was expected to see similar gains when trading restarts .
Treasury Secretary Jack Lew was the first U.S. official to speak on Thursday, warning that the standoff was stressing financial markets but that prioritising government payments just to avoid hitting the debt limit would be irresponsible.
UniCredit's Global Head of FX Strategy Vasileios Gkionakis said positive signals for the dollar had been reinforced by minutes of last month's Federal Reserve meeting, published on Wednesday. They showed its surprise decision not to start scaling back its stimulus was a close call.
"The Fed minutes reiterated that tapering (of monetary stimulus) will happen during this year ... but I think it (rise in dollar) is largely that there are some discussions between the Republicans and Democrats" over the debt ceiling, he said.
Both U.S. political parties floated the possibility on Wednesday of a short-term increase in the country's $16.7 trillion debt limit to avoid a default and allow time for broader negotiations on the budget.
With the dollar heading up, the euro was already on the back foot, and there was further pressure after both French and Italian industrial production figures fell short of expectations.
Swedish industrial output also fell, a day after Britain's did the same, a reminder that the broader region's economic recovery remains delicate.
The euro was hovering near a two-week low of $1.3500 versus the dollar, while sterling dropped to a three-week low against the greenback and a five-week trough against the euro.
DEAL OR NO DEAL
With the U.S. government shutdown limiting the usual steady flow of data, economists were eyeing the weekly release of privately compiled jobless claims data due at 1230 GMT for any flavour of the impact the political deadlock is having.
In Asian trading, Tokyo's Nikkei share average advanced 0.9 percent to its highest in a week, while shares elsewhere lost ground.
Investors have expected the Republicans and Democrats to cut a deal by an Oct. 17 deadline to raise the debt ceiling, though each day that passes without an agreement tests their nerves.
It is unclear how long a short-term deal would be effective for, but any move to raise the borrowing limit would at least stave off a possible default.
"It's a step forward for the market to resume risk-taking, though we are not too optimistic," said Isao Kubo, an equity strategist at Japan's Nissay Asset Management. "Investors are cautiously buying back."
Strains in short-term U.S. interest rates and funding markets have also increased as the deadline nears.
There were few signs of nerves on European bond markets, however, with German government bonds typically favoured by risk-sensitive investors edging lower and higher-yielding euro zone periphery debt faring better.
News that the Federal Reserve's decision last month not to reduce its $85 billion-a-month bond-buying programme was a "close call" helped buoy the U.S. currency.
"This is consistent with our expectations that the Fed will taper purchases at the upcoming December meeting," Barclays Capital said in a note. "That said, the ongoing federal government shutdown and upcoming expiration of the debt ceiling suggests that the decision to taper could be pushed into 2014."
As the dollar regained its footing, gold eased 0.3 percent to around $1,302.7 an ounce, adding to Wednesday's 0.9 percent decline.
Oil rose on news Libya's prime minister had been seized by armed gunman in a Tripoli hotel although he was later freed.
Brent headed towards $110 a barrel and U.S. crude prices added 0.5 percent to about $102.19 a barrel. U.S. prices had tumbled 1.9 percent on Wednesday after the largest weekly build-up of U.S. stocks in a year added to the worries of a market already concerned about the budget deadlock.