Consumer group Which? said nearly half of its members surveyed said such reassurance was most likely to make them see red while hanging on the line.
Next on the frustration list was being directed to the company's website, and apologies for all operators being busy.
Callers would rather be told how long they would have to wait, Which? found.
Many also wanted to know where they were in the queue, and to be given the choice of being called back. Nearly half of those asked said that classical music was the most soothing while waiting.
Nine in ten of those asked felt that they were prepared to wait on the line for no longer than five minutes.
Richard Headland, editor of Which? magazine, said: "Waiting on hold is a waste of time, but some organisations make the experience needlessly annoying through objectionable messages and music.
"If these drive you round the bend, vote with your feet and take your custom elsewhere. The best companies know the value of answering your call quickly."
Businesses lining up a queuing strategy
Jo Causon, chief executive of the Institute of Customer Service, a trade body, said: "People are time-poor and less likely to be happy waiting for service as a result. It means consumers are less understanding of organisations that do not make it easy to get in touch.
"If businesses want to enjoy ongoing customer loyalty - and attract new business - their focus should be on convenience and efficiency. In short, this means getting it right quickly, and getting it right first time. Anything less, and customers will think twice about spending money or recommending them to others."
She pointed out that the phone is now consumers' third most popular method for getting in touch with an organisation, behind face-to-face contact and online.

The charity said job security fears and benefit cuts pushed the number of people seeking help from its volunteers to more than 160,000 last year.
Text messages were up by 22% in 2013 with a 7% increase in emails answered.
Executive director for Wales Sarah Stone said the charity wanted to keep promoting the benefits of talking.
The call came as the Samaritans published its Impact Report for 2013/14, detailing the outreach work of the charity's nine branches in Wales.
Nearly 700 volunteers in Wales were involved a range of activities to tackle suicide, including:
"Against a backdrop of difficult economic times and where a disproportionate number of those who take their lives are struggling with social and economic deprivation, we need to convince people that talking about what's troubling them is valuable and potentially life-saving," said Ms Stone.
"It is something we all need to do and encourage other people to do."
She added: "The demand for our service is increasing. We took a call every three minutes last year in Wales.
"It is important that we keep working to raise awareness of our service and the benefits of talking."
While most help was given via phone, letter or face-to-face support, the Samaritans said contact via newer methods such as text and email was growing.
"We also need to keep evolving and finding new ways to reach out to people, continuing to be accessible to all who desperately need our service," said Ms Stone.
The Samaritans said the number of calls for help across the UK and Ireland also reached a five year high in 2013 of 5.23m.
Launching the report, Health Minister Mark Drakeford said: "I am grateful to Samaritans for its continued work in support of suicide prevention.
"It is a key partner and plays a vital role in delivering Talk to Me, the national action plan to reduce suicide and self-harm in Wales.
"We want people to feel able to support their friends, family members and colleagues who, for a variety of reasons, may be at risk of suicide.
"Ultimately, we as individuals, colleagues or friends, all have a responsibility to listen to and support those close to us."
Being told that your call is valued is the most annoying feature for those waiting on the phone to a company, a new survey suggests.
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Money worries are blamed as a key cause of suicidal feelings as the Samaritans in Wales report their highest number of calls for five years.