The project, Europe's largest transport scheme, was due to open in December 2018 but has been beset by delays.
The additional costs on the Network Rail-run section of the line are not related to the coronavirus pandemic.
A new funding package will need to be developed with "London as the primary beneficiary bearing the cost", Railways Minister Chris Heaton-Harris said.
Mr Heaton-Harris called the cost increase and schedule delays "very disappointing".
Delays in upgrades to stations and provision of power are behind the extra cost.
The cost of the surface lines either side of the tunnels, run by Network Rail, now stands at just under £3bn.
This is in addition to the £650m extra funding agreed last November for the Crossrail project as a whole.
Work has now restarted on Crossrail sites following a pause due to coronavirus.
The London Assembly Transport Committee said: "We knew costs were increasing before Covid hit. It now seems almost certain that the project will be further delayed and put further into the red as a result of this crisis."
source: BBC News
Crossrail needs an additional £140m to complete its surface lines, the government has announced.