The government is to meet this week with Southern, which links London with Surrey, Sussex, Kent and Hampshire.
The rail company is embroiled in a long-running union dispute over the role of guards on new trains.
Mr Maynard said the continued delays and cancellations affecting the service were "unacceptable".
More updates on BBC Live: Sussex
Industrial action by the National Union of Rail, Maritime and Transport Workers (RMT) and high levels of staff sickness have hit services, with the introduction of a temporary emergency timetable initially cutting up to 341 trains a day.
Mr Maynard told the Commons: "Some routes are still suffering badly and my priority is making sure services are being restored in a timely, sensible and lasting manner."
"The real solution here is for the RMT to bring this dispute to a close and start to put passengers first," he added.
Mr Maynard also denied plans for "more generous" compensation to Southern Rail commuters affected by strikes were on the "backburner".
He also agreed to consider calls for season ticket holders to receive a rebate of up to 20%.
Meanwhile, Southern announced it would reinstate the full timetable from Tonbridge and Reigate to Redhill and London Victoria/London Bridge on Monday.
Alex Foulds, Southern's passenger services director, apologised to customers "who have suffered ever since the RMT began their unnecessary action".
He said the temporary weekday timetable had been delivering a "more consistent, reliable" service.
"We are steadily reintroducing trains and will continue to do so until the entire timetable is back in place," he added.
Mick Cash, RMT general secretary, called the changes "pitiful".
He added: "The fact passengers are still paying through the nose for a vastly reduced service is solely due to the gross managerial incompetence and profiteering of this basket-case rail operator.
"Yet again Southern are blaming their staff for their own systemic failures..."
RMT spokesman Garry Hassell has said the dispute "could last until Christmas".
Rail Minister Paul Maynard has assured passengers he is determined to resolve issues on the troubled Southern network as a matter of urgency.