The Mid Yorkshire NHS Hospitals Trust is trying to close the Friarwood Birth Centre after claiming it is underused.
The trust has cited figures showing that fewer than 200 births a year take place at Pontefract, compared to nearly 6,000 at Pinderfields Hospital in Wakefield.
But Normanton, Pontefract and Castleford MP Yvette Cooper has disputed the numbers, suggesting they have been influenced by temporary closures of the unit and uncertainty among mums-to-be.
In a strongly-worded address to trust officials at a health scrutiny committee, Ms Cooper said the public's confidence in the process had been "undermined".
She said: "The trust is not being straight with the community or the committee about the figures.
"What’s very clear is that this is a result of the repeat closures during the summer and the repeated uncertainty.
“When you have anecdotal evidence of mums being rushed out of Pontefract to Pinderfields, it’s no wonder mums are feeling a little bit insecure about Pontefract and wondering if it’s safe.
"I think this gap in the figures just seems to be driven by the trust and the decisions they want to make, rather than the decisions of local mums.
"Pontefract is a growth area. More housing developments are being built.
"That suggests we should be moving in the opposite direction to this and growing services, rather than shrinking them as the trust is seeking to do.
"It's always the Five Towns that get hit. We just want a fair deal."
The trust has reversed a previous decision to stop taking any more bookings from pregnant women who want to have their babies at Pontefract. Ms Cooper said that would have seen the unit "closed by stealth" by the end of February.
Earlier this year, the trust's chief executive firmly denied suggestions people were being diverted from Pontefract Hospital to Pinderfields, insisting that all patients had freedom of choice over where they were treated.
At Thursday's meeting, director of nursing David Melia said that the recruitment of 15 extra midwives in the autumn meant that the service at Pontefract was "as sustainable and as active as we can make it".
He said: "We are probably in the best place we’ve been for a long time in having a very nearly full establishment of midwives.
“We do have issues with long-term sickness and short-term sickness across the service but we have more midwives than we’ve had in a very long time.
"Women will now have the option to use Friarwood as a place to give birth. We won't put that pause in now.
"During this period if people are booking to go to the Pontefract unit that’s what we’d want to honour."
The trust and officials from Wakefield Clinical Commissioning Group (CCG) will meet with NHS England next week to make the case for closure. A formal consultation with the public will then get underway.
The entire process is expected to take several months, with the unit remaining open for the timebeing.
The CCG's deputy chief officer Pat Keane said: "There’s no final decision and there will be no decision to close the midwifery-led unit prior to any formal engagement or any consultation.
"The unit at Pontefract is open and it’s running."
The trust has also denied repeated claims from councillors that the whole of Pontefract Hospital is being "wound down" and primed for closure.
But speaking after the meeting, Pontefract South councillor David Jones called for more clarity.
He said: "The trust needs to say exactly what their position is on how they see the future of services at Pontefract Hospital in relation to their other sites.
"So far they've failed to address that."