LONDON, Oct 2 (Reuters) - The pile of negative yielding euro zone government bonds rose in September to just over 6 trillion euros from around 5.4 trillion a month earlier, Tradeweb data showed on Friday, the latest sign that global uncertainty has renewed demand for safe assets.

A rise in COVID-19 cases in Europe, concern about the economic outlook and unease ahead of a looming U.S. election has pushed down sovereign bond yields globally.

In Europe, where 10-year German bond yields notched up their biggest monthly fall in five months in September, that has meant an even deeper push into negative-yield territory.

According to Tradeweb data, around 68.6% or just over 6 trillion euros of the 8.9 trillion euro government bond market had negative yields as of the end of September.

That was up from around 62% at the end of August and marked the highest share of negative-yielding debt on the platform since September 2019.

"Euro rates are moving lower again and there are lots of reasons for that but a big one is that inflation and inflation expectations are weak and that's increasing expectations for more ECB easing and cementing the negative-yielding bond pile," said Antoine Bouvet, senior rates strategist at ING.

The pool of negative-yielding investment grade corporate bonds also rose to stand at around 997 billion euros as of the end of September, or nearly 29% of a total market worth around 3.4 trillion euros, Tradeweb said. That was up from 872 billion euros as of the end of August.

Roughly 49% or 1.2 trillion pounds ($1.55 trillion) of UK government bonds traded on the Tradeweb platform of a total market worth almost 2.5 trillion pounds had negative yields as of end-September. That was up marginally from August.

(Reporting by Dhara Ranasinghe; Editing by Kirsten Donovan and Raissa Kasolowsky)