Ms Cullen described the meeting as “very productive”
The director of the Royal College of Nursing (RCN) says she does not have enough reassurance about safe staffing to propose an end to strike action.
Health workers in Northern Ireland have been staging industrial action in protest against pay and staffing.
Trade unions had a “positive” meeting with Health Minister Robin Swann on Tuesday, who offered £30m to restore pay parity among health workers.
But the RCN’s Pat Cullen told BBC News NI “there is still work to do today”.
- Health unions to consider £30m pay offer
She said it was “deeply concerning” that after the meeting she spoke to departmental officials who said that there “may be difficulties with the minister committing to the issues of safe staffing”.
Nurses are due to strike again on three days next week – Monday, Wednesday and Friday.
Ms Cullen said she could not suspend planned strike action for next week unless there is “a formal commitment on safe staffing that will deliver for patients and nurses”.
“At this point in time, I do not have enough detail and reassurance that I could put to the Northern Ireland board and propose that we suspend our strike action,” she said.
The Northern Ireland Public Service Alliance (NIPSA) union said industrial action “will remain in place until this dispute is resolved to the satisfaction of members”.
Speaking on BBC Radio Ulster’s Good Morning Ulster programme, the new health minister said he would meet the unions later on Wednesday for further clarity.
He said he thought reassurances “had gone far enough” but he would work with health unions and added that there were “no guarantees about the financial package that is coming”.
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Media captionHealth strike: Robin Swann confirms pay package for nurses and health workers
But he stressed his commitment to health staff who he praised for the care they showed his son, who was born with a heart defect.
“I owe so much to our health service, and when the health portfolio came up, I couldn’t pass it by personally because of what we, as a family, owe to our NHS,” he said.
Arlene Foster, Robin Swann and Michelle O’Neill pictured alongside health workers on Tuesday
On Tuesday, the unions expressed concern that the money is coming from Stormont’s finances and not additional funding from Westminster.
They are expected to respond to the pay offer on Thursday.
Nurses and healthcare workers began industrial action over staffing levels and pay, which does not rise in line with healthcare workers in Scotland, England and Wales.
Unions have not indicated that the strike action will be called off
On Tuesday, Finance Minister Conor Murphy said he recognised the updated pay offer was coming from within existing Stormont finances, but said it was not a case of “robbing peter to pay Paul”.
He said as the executive had not yet been able to tie down funding commitments from the British government, they had “dipped into existing finances”.
He added that the proposed financial support was “way short” of what was expected.
BBC News NI political correspondent Enda McClafferty said he understood that the financial package was £2bn.