By Krisztina Than and Anna Koper

BUDAPEST/WARSAW (Reuters) - Wary of German Chancellor Angela Merkel's ambition for closer European Union integration, right-wing politicians in the EU's eastern wing are touting her weak election victory as a vindication of their concerns.

Eurosceptic governments in Poland and Hungary have been vocal in criticizing Merkel's 'open-door' approach to migration and opposing EU reforms that would transfer more power to the Brussels institutions at the expense of national governments.

Poland's foreign minister said Germany's Sept. 24 election, in which Merkel's conservative bloc won the lowest number of votes since 1949, was proof that Berlin would have to heed the concerns of eastern member states.

"She should focus on maintaining the unity of the European Union," Witold Waszczykowski told Polska the Times newspaper. "Mrs Merkel will have to look for new allies -- and this in turn opens room for maneuver for Polish diplomacy."

"Today, there is no climate for federalization and there won't be one in the nearest future."

Merkel is expected to take months to build a new coalition government, reducing German pressure on Warsaw and Budapest to comply with EU standards.

Her most likely coalition allies are the increasingly eurosceptic, pro-business Free Democrats and the Greens - but she also faces a more divided Bundestag lower house, where the anti-immigrant Alternative for Germany (AfD) is now the third biggest party.

Nationalist politicians in the EU's eastern member states hope the rise of the AfD, the first far-right party to enter the Bundestag in decades, will force Merkel to harden her stance on immigration after Germany admitted more than one million migrants and refugees, mostly Muslims, in 2015-16.

PROTECTING EUROPE'S BORDERS

Hungary has already said German politicians since the election have endorsed its measures to beef up its border security to discourage migrants from entering the EU.

"About some aspects of illegal migration we are still in debate, but there is full agreement on the principal issue that the protection of the external borders of Europe is very important," Foreign Minister Peter Szijjarto said after meeting senior German lawmakers in the city of Stuttgart last week.

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The head of the European Commission, Jean-Claude Juncker, has invited the leaders of the four 'Visegrad' states - Poland, Hungary, the Czech Republic and Slovakia - to a dinner in Brussels on Oct. 18, ahead of an EU summit, to try to ease tensions between them and wealthier western Europe.

Hungarian Prime Minister Viktor Orban's Fidesz party and Merkel's CDU-CSU are in the same political family in the European Parliament, and despite Berlin's criticism of his record in government, has welcomed Merkel's election victory.

"Let's quietly pray every evening for the extension of the mandate of the current chancellor," he said before the election.

Orban himself faces an election next April in which he will seek a third consecutive term, and he probably does not want to tackle EU reform issues head-on now, analysts said.

"Orban's objective is to keep the margin of maneuver open ​as long as possible: he does not want to face yes-or-no questions like whether to take Hungary into the euro zone or stay on the periphery anytime soon," Botond Feledy, senior fellow at the Centre for Euro-Atlantic Integration and Democracy in Budapest.

GERMAN-FRENCH AXIS

But once Merkel has bedded down a new coalition in Berlin, Budapest and Warsaw can expect a resumption of pressure over their record on democracy and rule of law from a reinvigorated partnership between Germany and Emmanuel Macron's France.

Analysts said Merkel and Macron, both keen to overcome EU disunity, may try to pick off more cooperative eastern states such as Slovakia and the Czech Republic in order to concentrate pressure on Poland and Hungary to comply with EU rules.

Merkel may also in due course revive her demands on the eastern states to take in more migrants as she seeks to blunt the allure of the AfD at home for conservative German voters.

Warsaw, currently under an unprecedented EU investigation over its rule of law standards, is bracing for renewed criticism.

"We are expecting Merkel to get tough on Poland - definitely not in the next few months while the new government is being formed, but after the domestic dust has settled," a Polish government source added.

(Writing by Krisztina Than, additional reporting by Robert Muller in Prague and Tatiana Jancarikova in Bratislava, Lidia Kelly in Warsaw; Editing by Gareth Jones)