Immigration and Work and Income are among the hardest agencies in the country to get on the phone.
Consumer New Zealand compared hold times for 16 government agencies, and found the average wait was 25 minutes and the organisation says it's not acceptable that New Zealanders are having to "put their lives on hold" to access essential services.
Work and Income took 90 minutes to answer, while Immigration New Zealand took two-and-a-half hours across four different attempts.
At the other end of the spectrum, Inland Revenue, CERT and NZ Customs all answered the phone within two minutes.
On average, Consumer NZ said private businesses answered the phone twice as fast as government agencies.
Consumer head of content Caitlin Cherry said the investigation focused on 16 government agencies, with all calls made on a weekday between 9am and 5pm.
"We were surprised that we had to call some government departments multiple times because either the first number we tried wasn't the right one, or we were hung up on," she said in a statement.
When attempting to contact Immigration: "Firstly, we had the wrong number for calls from mobile phones," Cherry said.
"On our second attempt our call dropped out after about an hour and a half on hold. On our third attempt the call centre was not accepting calls. Finally, after a fourth attempt, and another hour and 10 minutes on hold, we got through to an operator.
"The Human Rights Commission was the only agency where we couldn't reach a human. We tried two different menu options in our efforts to speak to someone, but we were advised to leave a voicemail."
While Consumer understood government contact centres services were in demand, "we don't think it is acceptable for New Zealanders to have to put their lives on hold to access essential services," Cherry said.
"Our investigation has found, in some cases, that's precisely what's happening."
Some agencies were upfront and transparent on their websites about the wait time a caller was likely to face, Consumer said.
"The accuracy of the estimated call wait times varied, with only one agency overestimating the wait time," Cherry said.
"Immigration NZ picked up 22 minutes earlier than expected, but it was still an agonisingly long wait to speak to someone.
"NZTA, StudyLink and Work and Income all underestimated their call wait times, with the caller on hold at least 10 minutes longer than anticipated."
The investigation found that having identifier information at hand, such as a client number, could significantly shorten the time on hold.