Last month, Brussels recommended holding up €7.5 billion of EU funds for Budapest over alleged corruption concerns. Hungary has repeatedly blocked major EU initiatives since then.
What do we know about the deal?
The compromise with the government of right-wing Hungarian Prime Minister Viktor Orban means the EU can meet its promise to keep supporting Ukraine as it fights Russia's invasion.
It allows Brussels to still exert some pressure on Hungary over Budapest in a long-running dispute with Orban over concerns about the rule of law and democracy there.
The agreement frees up some €1.2 billion for Hungary, but Orban will still need to convince his fellow EU members that he has carried out key reforms to obtain the remaining €6.3 billion.
The freezing of EU funds to a member state over concerns about democracy is unprecedented. The EU is also holding back some €5.8 billion of post-COVID-19 EU recovery money because of Hungary's democratic backsliding and concern about judicial independence.
Anna Lührmann, a junior minister in Germany's foreign office responsible for Europe and climate, called the decision "a very important signal for strengthening the rule of law in Europe." However, Lührmann also said Berlin had hoped for more funds to be held back pending reforms.
The agreement reached on Monday also saw Budapest agree to a minimum 15% corporate tax that it had been blocking.
That initiative is not only an EU one but involves some 137 countries, including the United States. The agreement's aim is to prevent large corporations from shifting their profits to regions with lower taxes and for multinational businesses to pay more tax where they operate.
As well as reducing the amount of regular funding that was frozen, EU countries agreed to take a step towards giving the post-coronavirus aid to Budapest.
EU negotiator Tibor Navracsics told a news conference on Tuesday that Hungary hoped to sign funding agreements with the European Union within days to unlock billions of euros worth of recovery money and development funds.
He said the Hungarian parliament would pass another tranche of legislation needed to access the funds by the end of March.
NATO accession on cards for Finland, Sweden
Meanwhile, Orban's chief of staff, Gergely Gulyas, said the Hungarian legislature would start debating the ratification process of Sweden and Finland's NATO accession on February 20.
While the 28 parliaments of other NATO countries have already ratified the accession of Finland and Sweden, the legislatures of Turkey and Hungary have yet to do so.
Orban said late last month that Hungary would support Finland's and Sweden's NATO accession and parliament would set this item on its agenda at its first session next year.
Hungary's government is thought to have also been using the NATO membership issue as a lever in its dealings with the EU, of which Finland and Sweden are both members. The two Scandinavian countries stayed neutral during the Cold War but have moved to join NATO following Russia's attack on Ukraine in February this year.
Hungary has the closest relations with the Kremlin of any EU country, receiving oil through a pipeline from Russia that remains outside the scope of a bloc price cap.
rc/dj (AFP, dpa, AP, Reuters)