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(Changes dateline from Singapore, updates throughout)
By Dhara Ranasinghe
LONDON Sept 29 (Reuters) - World shares were broadly higher on Friday, but were set to end September with their worst quarterly performance in a year, haunted by worries over elevated interest rates.
European shares rose, helped by gains for luxury stocks, and U.S. equity futures pointed to a firm start for Wall Street later in the day .
Yet, as the third quarter drew to a close, world stock markets were left nursing heavy losses on rising bond yields.
Bond markets were broadly stable, but are also ending a torrid quarter. Euro zone government bond yields, which along with U.S. Treasury yields have hit fresh multi-year highs this week, are heading for their biggest quarterly rise in a year.
"Yields are way to high and will move lower but we're in that gap between now and when that happens," James Rossiter, head of global macro strategy at TD Securities in London, said.
"It feels like (10-year U.S. Treasury) yields could break up to 5% but ultimately they will move lower."
In London trade on Friday, the 10-year U.S. Treasury yield was down 5 basis points (bps) at 4.54%, having risen to a 16-year high on Thursday.
Germany's 10-year government bond yield, the benchmark for the euro area, fell 10 bps to 2.86% after jumping 13.5 bps the day before. It was still set to end the week up 14 bps, in its biggest weekly rise since early July.
Meanwhile, British government bonds, which also sold off sharply on Thursday, recovered.
Britain's economic performance since the start of the COVID-19 pandemic has been stronger than previously thought, with faster growth than Germany or France, according to revisions to official data released on Friday.
Asian shares gained over 1% in their best day in weeks , but were still on track for their worst quarterly performance in a year, as were European shares and the MSCI's world stock index.
Japan's Nikkei closed a touch lower, while Chinese markets were closed for a holiday and are on a break next week.
Chinese property remained in focus after China Evergrande Group said its founder is being investigated.
Investors are watching out for the U.S. personal consumption expenditures price index and euro zone inflation data.
There was also a focus on Washington where the Democratic-led U.S. Senate forged ahead on Thursday with a bipartisan stopgap funding bill aimed at averting a fourth partial government shutdown in a decade, while the House began voting on partisan Republican spending bills with no chance of becoming law.