If Parler fails to find a new web hosting service by Sunday, the entire network will go offline.
Jake Angeli, real name Jacob Anthony Chansley, is accused of violent entry and disorderly conduct.
The charge of “incitement of insurrection” is set to be tabled on Monday after riots at the Capitol.
Twitter says it banned the US president “due to the risk of further incitement of violence”.
Mr Trump is facing calls for his removal from office over the storming of Congress by his supporters.
Top Democrats call for the president to be removed as he commits to an “orderly” transition of power.
The US economy lost 140,000 jobs in December, as rising coronavirus cases took a toll.
The death of the officer, Brian D. Sicknick, appeared likely to lead to calls for profound changes to the Capitol Police, a centuries-old force.
There are calls for Donald Trump to be removed from office. How likely is it – and could he pardon himself?
Brian Sicknick died after sustaining injuries during the pro-Trump violence at the US Capitol.