* Wall St shares recover from Russia Gate worries, but dollar hurt
* Fed's Brainard suggests rate hike depends on inflation
* Oil extends gains on U.S. production fall, stockpiles data
TOKYO, July 12 (Reuters) - Asian shares gained on Wednesday after Wall Street managed to weather a fresh twist in the controversy over U.S. President Donald Trump's alleged connection with Russia, while investors looked ahead to Federal Reserve Chair Janet Yellen's comments.
MSCI's broadest index of Asia-Pacific shares outside Japan ticked up 0.4 percent. Japan's yen-sensitive Nikkei slid 0.3 percent on the yen's gains but MSCI's dollar-denominated Japan index gained 0.4 percent.
U.S. stocks took a brief tumble after emails disclosed Trump's eldest son welcomed help from a Russian lawyer for his father's 2016 election campaign against Hillary Clinton.
But by the closing bell, Wall Street shares had clawed back their losses.
"The e-mails look pretty bad but then again they don't look like decisive evidence (for illegal behaviour) either. I doubt this alone would lead to a risk-off market," said Hiroko Iwaki, senior fixed income strategist at Mizuho Securities.
U.S. shares were helped in part as the Senate announced a two-week delay to its August recess to allow more time to tackle a measure that would repeal key parts of Obamacare, as well as pursue other legislative priorities.
Still, it remained unclear whether U.S. Senate Republicans have the votes to pass the measure or even what form it would finally take.
On the other hand, the dollar failed to recover after the damage suffered from the new twist in the Trump campaign's alleged links with Russia.
The euro vaulted to a 14-month high of $1.1484 in Asian trade.
The dollar also lost steam against the yen, which had been under renewed pressure following Friday's bond-buying by the Bank of Japan which highlighted divergent monetary polices between the two countries.
The U.S. currency dropped 0.3 percent to 113.60 yen, slipping from a four-month high of 114.495 yen touched on Tuesday.
The dollar index against a basket of six major currencies was hovering at 95.64, within sight of its nine-month low of 95.47 plumbed at the end of June.
U.S. Treasuries yields stayed below their recent peaks, with the 10-year yield at 2.355 percent, compared with 2.398 percent marked on Friday, its loftiest level in almost two months.
Ahead of Fed Chair Yellen's testimony to Congress on the state of the U.S. economy from 1400 GMT, two of her colleagues cited low wage growth and muted inflation as reasons for caution on further interest rate increases.
Fed Governor Lael Brainard embraced the plan to reduce the balance sheet "soon," but suggested her support for any future rate increases will depend in part on how inflation shapes up.
Minneapolis Federal Reserve Bank President Neel Kashkari said he finds it hard to believe that the U.S. economy is in danger of overheating when wage growth is so low.
Traders trimmed expectations of a rate hike by the end of the year, with dollar interest rate futures pricing in about a 55 percent chance compared to about 60 percent earlier, while most investors expect the Fed to decide to start shrinking its balance sheet in September.
"Yellen has indicated after the June policy meeting, in the clearest way as possible by her standards, that she plans to start balance sheet reduction and there will be one more rate hike this year. Since then, there's been no big changes in the economy," said Tomoaki Shishido, senior market economist at Nomura Securities.
"I would think the U.S. CPI data on Friday could be more important. If the Fed's assessment that the softness in CPI between February and May is transitory, the Fed will go ahead with its plan. If that's not the case, some Fed policymakers will want to revise that plan," he added.
Reaction was largely muted to a story by Politico that Trump is increasingly unlikely to nominate Yellen next year for a second term, and National Economic Council Director Gary Cohn is the leading candidate to succeed her.
Oil prices extended gains from the previous day as the U.S. government cut its crude production outlook for next year and as fuel inventories plunged.
U.S. crude futures rose 1.6 percent to $45.75 per barrel, extending their recovery from Monday's near two-week low of $43.65. Brent futures gained 1.4 percent to $48.16 per barrel.
Both contracts have risen above their 50 percent retracement of their fall between mid-last week and Monday.
(Editing by Shri Navaratnam and Jacqueline Wong)