Investors appear to hope May's pending resignation could unblock the political stalemate over Brexit. Some analysts are warning it could simply mean another delay to the EU departure.
Britain's FTSE 100 rose 0.6% to 7,276 in midday trading and the pound rose to $1.2686 from Thursday's close of $1.2657. After May steps down, a new leader will be chosen within the ruling Conservative Party, a process likely to take several weeks. Some experts see a rising chance of a Brexit without a deal on trade relations, though others note that parliament remains as divided as before, and a new leader will find the same challenges to agree on a Brexit deal among U.K. lawmakers.
France's CAC 40 added 0.9% to 5,327, while Germany's DAX also rose 0.9% to 12,056.
U.S. shares also were set to open higher after President Donald Trump said he expects to meet with his Chinese counterpart Xi Jinping at a summit next month in Japan, raising hopes for progress in talks on the festering trade dispute between Beijing and Washington.
Future contracts for the Dow rose more than 0.6% to 25,627. The same for the S&P 500 added 0.6% to 2,837.
In Asia, the mood was less upbeat.
Japan's benchmark Nikkei 225 fell 0.2% to finish at 21,117.22. Australia's S&P/ASX 200 lost 0.6% at 6,456.00. South Korea's Kospi dropped 0.7% to 2,045.31.
Hong Kong's Hang Seng edged 0.3% higher to 27,353.93, while the Shanghai Composite was little changed at 2,852.99.
Stocks ended sharply lower on Wall Street on Thursday in a broad sell-off that left the benchmark S&P 500 index on track for its third straight weekly loss and had the Dow Jones Industrial Average down more than 400 points until late afternoon.
Traders sought safety in the bond market, driving bond prices higher, which pulled the yield on the 10-year Treasury to 2.31%, the lowest level in more than a year. It was at 2.33% at midday in Europe.
The stock market has been gyrating since Washington and Beijing escalated their dispute over trade this month. Now, the two sides have broken off negotiations and appear set for a long standoff. Investors are concerned that a prolonged trade war could stunt economic growth and hurt corporate profits.
ENERGY: Benchmark U.S. crude rose 66 cents to $58.57 a barrel in electronic trading on the New York Mercantile Exchange. It plunged 5.7% to settle at $57.91 a barrel on Thursday. Brent crude, the international standard, added 82 cents to $68.58 per barrel.
CURRENCIES: The dollar rose to 109.67 Japanese yen from 109.60 yen on Thursday. The euro strengthened to $1.1186 from $1.1182.
Matt Ott in Madrid contributed to this report.
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