Record numbers of parents with outstanding child support debts are being stopped from travelling overseas, with more than one parent a day being prevented from travelling at airports and sea ports until they pay.

The human services minister, Michael Keenan, said many of those stopped were able to immediately pay their debt, which he said showed they had the means to support their children but were choosing not to.

After being stopped at an airport last year, one parent paid $350,000 in a single payment. Another parent paid $60,000 on the spot, while, in a separate case, a parent who had been residing overseas and who returned briefly to Australia paid $30,000 in a lump-sum.

In the first 10 months of this financial year, 358 people were stopped at the point of departure and given a choice to pay the outstanding child support or cancel their travel plans. It already surpasses the previous record of 333 people who were prevented from leaving Australia during the previous financial year.

“If a parent can afford to take an overseas holiday ... they can and should be made to pay what they owe,” a statement from Keenan’s office said. “The welfare of their children should be their first priority, not getting a tan on a beach in Bali.”

The financial year so far has seen a record $10.4m repaid by parents about to leave the country. Keenan said many of those stopped had repeatedly ignored attempts by the Department of Human Services to help them pay through voluntarily repayment plans.

When a parent is stopped and pays the outstanding child support, the money goes to the department and it is then transferred to the parent who is entitled to receive the funds.

Most of those stopped were trying to leave New South Wales. Figures for the first nine months of the current financial year show 89 parents were stopped trying to leave that state, compared with 69 in Queensland, 51 in Victoria, 50 in Western Australia and 11 in South Australia. Thirty-seven overseas residents were stopped upon returning to Australia. Figures for the ACT, Northern Territory and Tasmania are not yet available.