Having recorded its steepest one-day drop since May on Monday, the S&P 500 stock index went on to post the biggest one-day jump since March a day later. It was set to end the week higher.
"Equity markets are signaling some symptoms of being tired after a long rally and recognise the peak growth environment," said Antonio Cavarero, head of investments at Generali Insurance Asset Management.
"But in the short-term real yields are still too low to provide an alternative, so the evolution of what happens next depends on COVID and the macro data."
IHS Markit's Flash Composite euro zone Purchasing Managers' Index, seen as a good guide to economic health, climbed to 60.6 in July from 59.5, its highest reading since July 2000. It was ahead of the 50-mark separating growth from contraction and a Reuters poll estimate of 60.0.
Europe's broad Stoxx 600 index was up 0.5% and set for a fourth straight day of rises, having tumbled more than 2% on Monday.
In contrast, MSCI's broadest index of Asia-Pacific shares outside Japan slipped 0.7%, leaving it down 1.4% on the week.
Japan's Nikkei was closed for a holiday, but off 1.7% for the week and a whisker away from a seven-month trough.
MSCI world equity index was steady after three straight days of gains.
Investors were already looking ahead to the Federal Reserve's policy meeting next week where more discussion about tapering is expected, though Chair Jerome Powell has repeatedly said the labour market remains well short of its target.
Powell argues that the recent spike in inflation will prove fleeting, which may be one reason bond markets have rallied so hard.
U.S. 10-year Treasury yields were up 1.6 basis points at 1.28%, having hit a five-month low of 1.128% early in the week.
German 10-year bonds yields, down 6 bps this week to -0.41%, kept near five-month lows after the European Central Bank on Thursday pledged not to raise rates until inflation was sustainably at its new 2% target.
"If we see substantive policy action in the months ahead to back up the new inflation goal, I would not be surprised to see bond yields push lower and market-based inflation expectations rise," said Katharine Neiss, chief European economist for PGIM Fixed Income.
The dollar was set to end the week with small gains after several volatile days when currencies were tossed by shifting risk appetite.
The dollar index was up 0.2% for the week, rising slightly on Friday to stand at 92.878.
Russia's rouble steadied ahead of the central bank's rate-setting meeting, which is expected to conclude with a sharp rise in interest rates.
Elsewhere, Brent crude oil was down 0.3% at $73.57 a barrel, after jumping overnight, while U.S. crude also fell by a similar amount to $71.72 per barrel.
(Reporting by Dhara Ranasinghe; Additional reporting by Wayne Cole in SYDNEY; Editing by Ana Nicolaci da Costa) ((Dhara.Ranasinghe@thomsonreuters.com; +442075422684;))