The announcement comes less than one week after the EU summit hailed as bringing unity to all but one of its member nations.
In Brussels, 26 of the 27 members of the EU backed new fiscal rules to keep budgets in line, with only the UK abstaining.
Neither Hungary nor the Czech Republic uses the euro, and tax harmonisation plans were not explicitly discussed as part of the changes at the summit.
Nonetheless Hungarian prime minister Viktor Orban and his Czech counterpart Petr Necas said they wanted to take active roles in negotiations, adding they are concerned the pact may take away their independence on tax policy.
Mr Necas said: “We support the solutions which result in the stabilisation of the eurozone.
Czech Prime Minister Petr Necas (L) is welcomed by his Hungarian counterpart Viktor Orban (R)
“But we are convinced that tax harmonisation would not mean anything good for
Stock markets dipped following the news, but the major European indices remained in positive territory.
Sky’s economics editor Ed Conway said the announcements from Budapest and Prague underlined the fact that Britain was not the only nation uncomfortable with the treaty – and that it is not a done deal yet.
“It’s not just those two countries that have issues with it,” he said.
“Whether you look across at Sweden, Finland, Denmark, Ireland – a number of countries’ representatives have gone back to their parliaments and have examined what’s in front of them and have said they’re not 100% pleased with what they’ve signed up to in some cases.”
Negotiations are due to continue until March, with the next EU summit expected at the end of January or early February.
Meanwhile, the eurozone is likely to slip back into recession next year, according to a report by Ernst Young.
The audit firm said it expects the economies of the 17 member countries to shrink in the first two quarters of 2012.
The report predicts growth of just 0.1% for the whole of the year and warns unemployment in the eurozone is unlikely to fall below 10% before 2015.
The warning was backed up by economic data from Markit suggesting output continued to contract across the 17-nation bloc over the past month.
Although the headline Purchasing Managers Index (PMI) figure rose slightly, at 47.9 it remained below 50 which separates economic growth from a slowdown.
FTSE 100 1-Day Chart
“The reforms agreed at the summit on December 9 were a step in the right direction and the response seems to have been mildly positive,” Ernst Young said.
It added: “Investors remain very concerned about the commitment and ability of eurozone governments to implement reforms quickly.”
However, the leading economist and chairman of Goldman Sachs Asset Management has expressed his confidence in the single currency.
Jim O’Neill told Sky’s Jeff Randall Live that European leaders would not give up easily, despite the continuing crisis in the eurozone.
Meanwhile, the head of Britain’s armed forces, General Sir David Richards, has said the eurozone crisis is of “huge importance” to defence chiefs as well as the City.
Chief of the Defence Staff General Sir David Richards
In a lecture to the Royal United Services Institute in London, he said: “I am clear that the single biggest strategic risk facing the UK today is economic rather than military.
“Over time, a thriving economy must be the central ingredient in any UK grand strategy.
“This is why the eurozone crisis is of such huge importance, not just to the City of London, but rightly to the whole country, and to military planners like me.”
He added: “The country’s main effort must be the economy. No country can defend itself if bankrupt.”
Ernst Young agreed that problems in the eurozone have impacted the UK but said the worst may be over for Britain.
Marie Diron told Sky News: “The eurozone is the main trading partner for the UK so it is in the interest of the UK that the eurozone is stable and growing and what we see is that the UK will probably see weak growth next year, although the bulk of the pain has probably already gone through.”