First Minister Rhodri Morgan says Welsh Assembly Government ministers remain "absolutely committed" to relocating hundreds of civil servants to Conwy.
The office is to be built on the former Hotpoint site
A new building near Llandudno Junction to accommodate 650 assembly government staff was due to be open in late 2008.
But the assembly government said there was "a short delay" for re-tendering. Costs had risen in a move to make the building more environmentally-friendly.
Meanwhile, work on a new £20m office in Aberystwyth is due to start next month.
A review into the project for the new Conwy office looked at improvements using green technology towards making it "carbon zero".
Mr Morgan said: "Enhancements relative to the original specification have pushed up the overall costs to the point where a fresh procurement process is now required, and that means a change to the construction timetable," said the first minister.
He added that the assembly government remained absolutely committed to the project.
"I want to reassure the people of north Wales that the Llandudno Junction office will commence as soon as the new procurement process has been completed," he said.
"This short delay will ensure that our staff working in the new north Wales office will benefit from a working environment of the very highest standard."
However, Mr Morgan did say that the decision on the way forward had taken longer than expected.
The new base is intended to raise the profile of the assembly government in north Wales.
'Pause and review'
It is to be built on the former Hotpoint site with a total of 650 people expected to work there, of whom 160 will be transferred from Cardiff.
They include staff from departments for children, education, economy, transport and health and social services.
HBG Construction Ltd was given the main contract to design the new office in May last year.
The assembly government estimated then that the cost would be less than £20m.
But a review began in February and news of the delay emerged in June.
The Aberystwyth office will accommodate staff from the assembly's rural affairs and heritage and economy and transport departments, as well as workers from the Forestry Commission and the Countryside Council for Wales.
The work at Ffordd Parc-y-Llyn is expected to be finished in spring 2009, and the building, which will house 535 staff, is set to open for business that summer.