The state of emergency in place since March 22 will now last until at least June 5, Abbas announced.
But movement between cities in the Israeli-occupied territory will be eased and steps taken towards reopening shops and other businesses, he added.
The measures do not apply to the Gaza Strip, another part of the Palestinian territories which is run by the rival Hamas-led government and where restrictions have already been eased.
So far there have been 345 confirmed cases of the novel coronavirus in the Israeli-occupied West Bank, with two deaths.
Israel has more than 15,000 cases and the Palestinian government is concerned that the tens of thousands of Palestinians working inside Israel could bring fresh cases, especially with the Muslim holiday of Eid Al Fitr at the end of the month