The Dow Jones Industrial Average and the S&P 500 remained in correction territory on Friday despite closing higher after another bumpy ride.
The Dow ended up 1.4% at 24,190 points, while the broader S&P was 1.5% higher at 2,619 points.
Both have fallen 10% from the record highs hit on 26 January, indicating a "correction".
Despite the positive finish, both indexes posted their worst weekly losses since January 2016.
Meanwhile, the Nasdaq Composite rose 1.4% to 6,874 points, giving the technology-focused index its worst week since February 2016.
"I don't think the market is focused on fundamentals at all – it's very volatile," said Anwiti Bahuguna at Columbia Threadneedle Investments in Boston.
In London, the FTSE 100 index ended the day down 1.1% at 7,092 points, bringing this week's declines to about 5%.
Other European markets also suffered on Friday, with Germany's Dax falling 1.4% and France's Cac 40 shedding 1.25%.
On Thursday, the Dow Jones fell by more than 1,000 points for the second time this week, and Asian markets followed the downward trend, with Japan's Nikkei 225 shares index closing down 2.3%.
The big sell-offs around the world this week have been pinned partly on concerns over the prospect of higher interest rates.
Bank of England deputy governor Ben Broadbent told the BBC that markets might have underestimated the prospect of a pick-up in inflation.
"If you look at what happened last year, particularly in the United States but also other equity markets, there was extremely strong growth – big rises in prices – as people gradually realised how strong the global economy was," he said.
"If markets are responding understandably to that growth, it's possible they weren't pricing in the risk that that same growth would produce some inflation and some rises in interest rates, and I think what you're seeing now is the effect of that realisation."
Why are markets falling?
The global sell-off began last week after a solid US jobs report fuelled expectations that the Federal Reserve would need to raise interest rates faster than expected, because of the strength of the economy.
That concern has prompted some investors to retreat from shares.
On Thursday, the Bank of England seemed to offer support for the view that rates in general are set to rise.
The Bank left interest rates at 0.5% at its meeting, but said a strengthening economy meant interest rates were likely to rise sooner than the markets were expecting.
Also worrying investors was a government budget proposal announced by US lawmakers, which raises spending caps and could fan inflation.
Bond yields in the US have also risen in recent weeks, typically a signal of higher rates.
Higher interest rates push up borrowing costs for companies and individuals, which can hurt corporate profits and curb economic activity.