Transport secretary Grant Shapps had earlier claimed the policy would be introduced "in future" when fully vaccinated people returned from amber list countries.
Labour called on Tuesday for a timeline for it to be introduced and questioned the lack of “concrete plans”.
Shadow transport secretary Jim McMahon said: “We have been pushing for the government to show international leadership, but so far they have failed to step up.
“So can I ask him why the government won’t bring forward concrete plans for an international vaccine passport which will be accepted by key destination countries?”
Labour has previously called for a green and red list, and the removal of the amber list.
Mr Shapps told the Commons there would not be an immediate resolution.
He said: “This is a complicated policy that requires time to work through.
"First, the Joint Committee on Vaccines and Immunisations has yet to opine on whether children should be part of the vaccination programme. They’re not at present and we must resolve how children would therefore be treated under a programme which enables people to travel.
“Next there’s the question of what to do for people who cannot be vaccinated for medical reasons or perhaps because they’re on one of the vaccine trials.
“There’s also the question of how to recognise vaccine status at ports and airports – easier for people who have been vaccinated in the UK, the main NHS app can already display your vaccine status, but less easy to prove from someone coming from overseas, particularly if they have paper-based systems.
“As a result of all of this we will announce to the House when we’re ready to make these decisions in order to bring this system into place, phased most likely for UK residents first.”
Mr Shapps also told MPs “progress is being made” on US-UK travel, but explained there were complications with licensing.
He said: “There are a whole series of complexities to resolve. For example, the US does not recognise AstraZeneca – currently because AstraZeneca hasn’t applied for the licence.
“On the other side we don’t have any particular system to recognise vaccine status from the United States because they don’t have a digitised system as we do with our NHS – they have 50 separate systems. There are complexities.”
The comments came in a session that also saw the Conservative chairman of the transport committee Huw Merriman demand a “flight path” for international travel, equivalent to the road map.
He asked: “For the domestic restrictions being eased, we have a road map with data and dates. For international travel can we have the equivalent – a flightpath so that we know what is going to happen and when and by what measure …. to give a little more certainty to industry and passengers alike?”
Mr Shapps replied: “I’ll certainly be very pleased to return to this House with further details as soon as next month.
"I share the absolute desire to return international travel as soon as we practically can to something as close as normality as possible, whilst recognising that it is important that we ensure that variants of concern are properly monitored are not brought into this country.”