Inland Revenue has asked customers not to call between 1pm and 3pm unless it's urgent as up to half its staff will be on strike then.
Commissioner of Inland Revenue Naomi Ferguson asked for customers to be patient and understanding during the strike today by PSA members.
The strike involves around 4000 staff of Inland Revenue and Ministry of Business, Innovation and Employment (MBIE), who are seeking better pay.
Inland Revenue's online services would be operating as normal during the stoppage but customers should get in touch by phone only if it was urgent, Ferguson said.
Some Inland Revenue offices may also be closed for appointments during the stoppages.
"We have plans in place to ensure critical work is prioritised. However, it is inevitable that there will be some reduction in service levels during these stoppages, particularly on our phone lines. I apologise in advance for that," Ferguson said.
"We remain committed to reaching an agreement with the PSA and getting good outcomes for all our people."
Agreements had been reached with the two other unions which represent staff at Inland Revenue, covering more than 1000 staff.
MBIE's human resources general manager Richard Griffiths said the ministry had
contingency plans in place and it was confident that any impact to customers and MBIE services would be minimal.
"We remain committed to continuing constructive discussions with the PSA and reaching an agreement that's acceptable to both parties at the earliest possible opportunity."
Staff at both government agencies are striking around the country.
"This isn't a decision our members have taken lightly but they feel they have no choice but to take industrial action," PSA national secretary Glenn Barclay said.
"We're asking for fair pay systems and a modest across-the-board pay increase but both employers have refused."
In Auckland, PSA members will block the central city intersection of Queen St and Victoria St for 40 minutes before marching to Freyberg Place for a rally.
Auckland Transport said it would manage the situation from the Auckland Transport Operations Centre. It would manage traffic lights as needed and would use social media to keep the public up to date.
Police said they would be monitoring the activity but didn't anticipate any traffic issues in central Auckland.
Marches and rallies will be held in other main centres including Wellington and Christchurch while in other towns and cities members have decided to do volunteer work.