After two days of sharp falls, a slightly firmer tone to world stock markets pushed most 10-year bond yields across the single currency bloc up around one basis point in early trade  .

Still, demand for high-rated bonds remained firm in a week that has seen more disappointing data from Europe and the United States, fears that a U.S.-China trade spat could become a more entrenched strategic dispute between the world's two largest economies and renewed uncertainty over Brexit.

British Prime Minister Theresa May is expected on Friday to announce the date of her departure, triggering a contest that will bring a new leader to power who is likely to push for a more decisive EU divorce deal.

"Today we are seeing a little back-up in yields but markets remain very pessimistic," said Pooja Kumra, European rates strategist at TD Securities in London.

"The risk-off tone was first led by Brexit then continued as we got weak data across the world."

Ten-year bond yields in the United States, Germany, Japan and Britain were all set for a third straight week of falls.

Germany's 10-year bond yield was up 0.5 basis points at minus 0.12%, keeping recent 2-1/2 year lows in sight.

"To be really bearish on Bund yields you need to expect the ECB to announce a balance sheet reduction and that's not going to happen for a few years," said Eric Oynoyan, G10 senior interest rate strategist at BNP Paribas.

The European Central Bank ended its asset purchase scheme at the end of last year but it reinvests funds from maturing bonds back into the market, keeping yields down.

U.S. Treasury yields were also higher on Friday after falling to their lowest levels since 2017 on Thursday .

Still, the yield curve as measured by the gap between three-month and 10-year Treasury yields remained inverted, in a sign of that investors are bearish on the economic outlook.

European parliament elections, which kicked off on Thursday, were in focus as investors weigh the possibility that eurosceptic groups could grab a third of seats, a level at which analysts say they could stir more trouble for governments and the economy.

The Labour party of European Commissioner Frans Timmermans on Thursday won a surprise victory in an Dutch election for European Parliament, an exit poll showed, easily beating a Eurosceptic challenger who had been topping the polls.