The dollar was firm against the yen on Friday as growing optimism on progress in US-China trade talks supported broader appetite for risk.

A Wall Street Journal report on Thursday that US Treasury Secretary Steven Mnuchin had considered easing tariff imposed on Chinese imports lifted sentiment though a Treasury spokesman later denied the report. “The reaction of the market to the report shows the overall optimistic view (is) spreading out across the foreign exchange market,” said Masafumi Yamamoto, chief currency strategist at Mizuho Securities.

Chinese Vice Premier Liu He will visit the United States on January 30 and 31 for the latest round of trade talks aimed at resolving the trade standoff between the world's two largest economies.

Against the yen, the dollar edged up to 109.31 yen for its fourth-day of gains against the Japanese currency and just off a two-week high of 109.40 touched overnight.

The dollar index, which measures the greenback against six major peers, was a shade higher at 96.088 after briefly rising to a near two-week high of 96.264 during the previous session. The index, which has been hobbled since late last year by the Federal Reserve's cautious stance on delivering further rate hikes, has managed to rebound from a three-month low of 95.029 touched just over a week ago.

The dollar held firm against the euro, while the pound was steady after rising overnight on hopes of a second referendum on Britain's membership in the European Union following Prime Minister Theresa May's crushing defeat in parliament of her Brexit deal.

Over the next week, focus will move to Thursday's release of January business activity figures for the eurozone, including French data, that will offer some clues on the health of the economic bloc, said Mizuho's Yamamoto.

French business activity plunged unexpectedly into contraction last month, retreating at the fastest pace in over four years in the face of violent protests against the government of President Emmanuel Macron.

“Once the dust regarding Brexit and the anti-Macron demonstrations clears, then I think the market will focus again on the beginning of the rate-hike cycle by the ECB (European Central Bank) toward the end of this year,” said Yamamoto. “If that'll be the focus, then I think there'll be a big shift from the monetary-policy cycle of the US to the euro area. That'll cause a broader weakness of the dollar and strength of the euro.”

The pound managed to held onto most of its overnight gains against the euro as traders wagered on a second referendum vote on Britain's EU membership.

While May has repeatedly rejected a second referendum, a vocal campaign in favour of holding a new vote has drawn the support of some lawmakers. Sterling was last down about 0.1 percent at 87.78 pence, trading close to a two-month peak of 87.60 scaled overnight. It was also firm against the dollar, trading at $1.2984 , not far off a two-month high of $1.3001.