They rose across the U.S. by at least 39,818 on Thursday, the largest one-day increase of the pandemic. The governor of Texas temporarily stopped the state’s reopening on Thursday as infections and hospitalisations surged.
But European shares opened higher, with the Stoxx 600 up 0.8% and London’s FTSE 100 up 1% at 0736 GMT.
The MSCI world equity index, which tracks shares in 49 countries, was up 0.3%, extending gains from late on Thursday.
The possibility of a second coronavirus wave and renewed lockdowns has limited market impact because if lockdown measures resume then markets expect this to raise the likelihood of more fiscal support for economies.
Having risen between 0500 and 0700 GMT, the dollar fell in early London trading to 97.317 against a basket of currencies by 0745 GMT.
The riskier New Zealand dollar was up 0.2%, having spent most of June at the level it was at before the coronavirus crisis for markets peaked in March.
Oil prices rose on Friday, extending gains on optimism about a recovery in fuel demand worldwide, despite signs of a revival in U.S. crude production.