It follows concerns that the BCG vaccine would not be available until later this year or early next year.
Health Minister, Leo Varadkar, said problems meant the vaccine, produced in Denmark, was not available.
He blamed production difficulties, delivery delays and sealing problems.
Carysfort Healthcare said it has been offered 40,000 doses of the BCG vaccine from the Canadian medical supply company, Intervax.
The delivery can be made in the next two to three weeks, but the offer will expire on 25 August due to shortages of the vaccine in other countries.
The Danish company is the only licensed supplier of the vaccine in the EU. However, according to Carysfort's managing director, Fintan Smith, the BCG offered is prequalified and approved by the World Health Organisation.
Mr Smith has been in contact with the Health Products Regulatory Authority in connection with the offer and whether it will allow the medicine to be used as an emergency as it is not licensed in the Republic of Ireland.
Sinn FÃ©in TD Gerry Adams had raised the vaccine's lack of availability after a Louth councillor from his party, Jennifer Green, who is due to give birth in three weeks, had been told her baby would not be given the vaccine as recommended by the Health Service Executive (HSE).
Mr Adams said the difficulties had been known by the Irish Department of Health since last year.
He said that, as a result of failing to find an alternative supplier, at least 50,000 babies, and potentially many more, would not receive their BCG when appropriate.
The Department of Health said other countries were experiencing similar delays in acquiring supplies of the vaccine from the Danish company.
The statement added that production was suspended in 2014 pending an extensive investigation regarding a possible problem with the capping of the vials.
It said the investigation had ended and product produced during 2014 was being released.
The statement also said the HSE would arrange appointments for children to attend clinics when the vaccine supply was restored.
The HSE said it had "no control over when BCG vaccine will be delivered by the vaccine manufacturer" and that "these supply issues will continue until at least quarter one, 2016."
A healthcare company in the Republic of Ireland said a Canadian firm has offered it 40,000 doses of a vaccine that protects against tuberculosis.