Campaigning for the upcoming vote, which overshadowed this week's central bank meetings, was temporarily halted after a British member of parliament was shot and fatally wounded on Thursday.
The recently volatile pound rose 0.5 percent in early Asian trade at $1.4273 with analysts noting the pro-membership MP's death could sway public opinion toward the "Remain" camp.
MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.5 percent, but was down nearly 3 percent for the week.
Wall Street marked gains overnight, with the benchmark S&P 500 index erasing sharp losses to snap a five-day losing streak.
Japan's Nikkei stock index gained 1.7 percent, taking back some of its steep losses. But Japanese shares were still poised to shed more than 5 percent for a week in which the perceived safe-haven yen soared after the Bank of Japan opted to stay the course on policy instead of mustering additional stimulus in the face of risks from waning inflation and weak global growth.
"In our view, these downside risks are already materializing, as evidenced by the decline in corporate inflation expectations and the recent slide in the BOJ's core inflation measures," HSBC economist Izumi Devalier said in a note.
"Continued inaction by the BOJ in the face of these risks only reinforces the market's suspicions that the central bank is running out of policy options, feeding back into a stronger yen," she said.
Japanese Finance Minister Taro Aso said on Friday that he was deeply concerned about "one-sided, rapid and speculative moves" seen in the currency market and that he would respond if necessary to ensure stability in currencies.
The dollar clawed back some lost ground on Friday, rising 0.5 percent to 104.75 yen, but it was still down more than 2 percent for a week in which it dropped as low as 103.555. That was its deepest nadir since August 2014.
The euro added 0.7 percent to 117.87 yen, but was still down more than 2 percent for the week. On Thursday, it plumbed a three-year low of 115.51.
The Federal Reserve also stood pat on policy on Wednesday, though it signaled it still planned to raise rates twice in 2016. But it also downgraded its economic view, and said slower growth would stem the pace of future monetary policy tightening.
Crude oil prices stabilised after they skidded about 4 percent to hit one-month lows overnight, on fears of that a possible Brexit could tip the global economy into turmoil.
Brent crude added 0.5 percent to $47.41 per barrel, while U.S. crude futures rose 0.3 percent to $46.35.
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