* Dollar extends gains against yen, euro * Nikkei rises to one-week high, U.S. stock index futures up * European shares seen opening higher * Gold falls, adding to Wednesday loss, as dollar strengthens By Dominic Lau TOKYO, Oct 10 (Reuters) - Japanese stocks rose to a one-week high and the dollar strengthened on Thursday as investors grew hopeful that U.S. politicians will resolve in coming days the fiscal impasse that has sapped market confidence. Tokyo's Nikkei share average advanced 0.9 percent to its highest point since the middle of last week, although shares elsewhere in Asia lost ground. The U.S. Standard & Poor's 500 E-mini futures added 0.5 percent, pointing to a firmer open on Wall Street. U.S. Treasury futures eased 13 ticks. Financial bookmakers expected major European indexes to open up as much as 0.6 percent. Investors have expected that a deal between the Republicans and Democrats would be reached by an Oct. 17 deadline to raise the debt ceiling, despite the partisan politics, although their nerves are tested each day that passes without an agreement. Republicans are considering signing on to a short-term increase in the government's borrowing authority to buy more time for negotiations on broader policy measures, according to a Republican leadership aide. It is unclear how long the increase would be effective for, but any move to raise the borrowing limit would at least stave off for now a possible debt default after the Oct. 17 deadline. "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 interest rates and funding markets increased as the deadline nears, keeping investors on edge. "We think a resolution to the debt ceiling impasse is increasingly likely to be a last-minute affair, and market anxiety seems likely to build up as we head into next week. We expect to see dollar/yen test lower in the days ahead," analysts at BNP Paribas wrote in a note. As the U.S. fiscal crisis escalated, Japanese investors sold a record amount of foreign bonds on a net basis last week, offloading nearly $23 billion worth. This "suggests that a reversal may be likely, as this scale of selling of foreign bonds is unprecedented and may well lead to renewed foreign bond purchases by Japanese investors if and when the U.S. fiscal crisis is resolved," Societe Generale said in a note. MSCI's broadest index of Asia-Pacific shares outside Japan slipped 0.2 percent, dragged lower by Chinese and Hong Kong stocks. China's CSI300 shed 1.1 percent and Hong Kong's Hang Seng Index lost 0.9 percent. BREATHING SPACE The dollar was up 0.4 percent at 97.785 yen, building on Wednesday's 0.5 percent rise as it pulled away from a five-week low earlier this week. News that the Federal Reserve's decision last month not to reduce its $85 billion-a-month bond-buying programme was a "close call" also helped buoy the U.S. currency. "This is consistent with our expectations that the Fed will taper purchases at the upcoming December meeting. 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," Barclays Capital said in a note. "A sooner resolution to the fiscal risks that cloud the outlook could keep December on the table, but a longer stalemate could dampen growth sufficiently and lead to a tapering in the first quarter of 2014 or later," it added. Against a basket of major currencies, the dollar gained 0.3 percent to 80.574, and is now almost a full point above an eight-month low hit a week ago. As the dollar regained its footing, gold eased 0.3 percent to around $1,302.5 an ounce, adding to Wednesday's 0.9 percent decline. U.S. crude prices added 0.2 percent to about $101.8 a barrel. Prices had tumbled 1.9 percent on Wednesday after the largest weekly buildup of U.S. stocks in a year added to the worries of a market already concerned that Washington's stalemate would curb demand in the world's biggest oil consumer.