"As with many large scale projects, Covid-19 has had a significant impact on the construction of the City Rail Link, including ongoing Covid-19 disruption impacting work sites, supply chain disruption (constraints, delays and extra costs with shipping), and higher than expected construction cost inflation," Wood said.
The project is being managed by its own entity, City Rail Link Ltd. The Auditor-General and CRL bosses have signalled the CRL will cost "significantly" more than budgeted.
The project is funded jointly by the Government and Auckland, who both pitched in to fund the last funding increase.
"The Government will match Auckland Council's contribution and we're committed to seeing this project through."
National's transport spokesman Simeon Brown said the Government could fund the increase if it spent less on other projects.
"With funding pressures continuing to increase in the construction and transport sectors it is critical the Minister of Transport stops wasting money on pet projects like cycle bridges, which are later cancelled, to ensure projects which are actually being delivered can get the funding they need," Brown said.
The CRL's cost increase was one of a number of cost pressures being felt in Auckland.
Auckland Transport's investment planning manager Tim Brown said last week the organisation was in the middle of "a perfect storm".
"We don't have sufficient funds at the moment to keep the public transport service operating as it is," he said.
Wood said the Government was still getting advice on just how far over budget the CRL might go.
"I am advised that the extent of this impact is ongoing and still being determined," Wood said.
Costs are currently split between the Government and the Council. It is not yet clear what mechanism will be used to fund any cost overrun.