The former world champions said on Monday, as cars from the other nine teams lapped Barcelona's Circuit de Catalunya, that they were unlikely to get on track until the third day.
"It is looking more likely than not that we will now not be in a position to run on track until Wednesday at the earliest," said deputy principal Claire Williams in a statement.
"This is obviously extremely disappointing, but it is unfortunately the situation we are in. We will be getting the FW42 on track as soon as we are able."
Williams finished last overall in 2018 with a car that scored a mere seven points from 21 races despite having the same engine as champions Mercedes.
The poor performance has meant less prize money for the team while the loss of Martini, replaced as title sponsors by telecom company ROKiT, and departure of other backers has also had financial implications.
Williams said on Sunday that they would be sitting out Monday's session.
"We have had an incredibly busy winter at Grove getting the FW42 prepared for the season ahead and, despite everyone’s best efforts, we need some more time before it will be ready to run," Claire Williams said then.
Williams have a changed line-up for the new season starting in Australia on March 17, with British rookie and Formula Two champion George Russell partnering Poland's Robert Kubica, who has returned from a near-fatal rally accident in 2011.
(Reporting by Alan Baldwin; Editing by Hugh Lawson)
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