A majority of Hungarians would support a referendum where they could vote on the Budapest 2024 Olympic and Paralympic bid, a survey which also claims only 46 per cent of citizens back the attempt has indicated.
This represents a decline on the 60 per cent figure who reportedly supported the idea of the bid in a similar survey in February.
Published in the daily left-leaning newspaper Népszabadság, the survey found 41 per cent opposed hosting the event while 13 per cent were neutral.
Using a sample of 1,000 people from across the nation, the investigation was carried out by market research company Ipsos on behalf of the left-liberal opposition Együtt Party, whose support for the bid has been notably more lukewarm than that of the governing Fidesz Party.
But its findings are broadly similar to those in another survey carried out by rival company Nézőpont Intézet last month in which 49 per cent were shown to back the bid while 42 per cent were against pressing ahead.
This will be a concern to Hungarian officials given the significance with which the International Olympic Committee (IOC) are giving to public support, falling a long-way short of a reported internal target of 70 per cent.
Further surveys are now expected to be conducted by the Hungarian Olympic Committee (HOC), as well as by the IOC themselves, with it still possible that the capital city could follow German contender Hamburg in calling for a public vote.
It would be virtually unprecedented if such a referendum was held across the entire country, with previous Olympic-bid questions having been confined just to the prospective host city itself.
As well as Hamburg and Los Angeles, Budapest was joined in a five-horse race last week by French and Italian capitals Paris and Rome following the official start of a two-year candidature process ahead of a decision being made in Lima in 2017.
Budapest is considered a strong-outsider but it hoping to take advantage of the IOC's Agenda 2020 reform process, which is said to increase the potential for new cities to bid.
But the process has begun at a difficult time, with Hungary in danger of being isolated within the European Union after the nation's Parliament voted this week to deploy troops to repel refugees from its border.
According to the IOC's Consultants Register, the city is also the only one of the five yet to appoint advisors for their bid, with many of the biggest and most experienced companies having already been snapped up by their four rivals.
But HOC officials remain confident of success, with director of international relations, Zsigmond Nagy explaining how a "Tender Committee" will now be set up to help prepare application documents ahead of the deadline of early next year.
Speaking on sports channel Sport7fő, he claimed the decision to launch a first Hungarian bid since the 1960 edition ultimately awarded to Rome will bring "self-identity" back to the nation, with IOC changes increasing their chances.
"A consultation tendering process has replaced the former competitive process, which, I think, gives us a great opportunity," he said.
"First, the Agenda 2020 reform program also gives the opportunity to Hungary.
"If you add that to the HOC articles of association it is an explicit objective that the Hungarian Olympic family will organise the Olympics at some point.
"The Olympics is not just the athletes but also the whole country moves, I am very proud that we are there [with the other] candidates."
The contest's next stage is expected to come this week when a series of “kick-off” meetings with the five Candidate Cities and their respective National Olympic Committees (NOCs) will be held by the IOC via video link.
September 2015: Budapest harbours genuine hopes for 2024 success due to Agenda 2020
September 2015: Bach confirms five cities in the running to host Olympics and Paralympics in 2024
August 2015: Budapest bid for 2024 Olympic and Paralympic Games supported by nearly half of Hungarians, poll claims
July 2015: Budapest 2024 seeking to break "monopoly" of largest and wealthiest countries hosting Olympics
July 2015: Hungarian National Assembly approves Budapest 2024 Olympic and Paralympic bid