BERLIN (Reuters) Germanys ruling parties have become rivals to form a government with the Social Democrats in a key western state, a development which is likely to deepen tensions in Chancellor Angela Merkels embattled coalition. Merkels conservative Christian Democrats had shared power in North Rhine-Westphalia with their federal coalition partner, the Free Democrats of Foreign Minister Guido Westerwelle, until an inconclusive vote on May 9. Having lost their majority, both sides have now signalled they could work with the centre-left Social Democrats in NRW, Germanys most populous state, even though it would complicate policy in Berlin and the FDP had explicitly ruled out such an option before the vote. The showdown in NRW follows weeks of unrest in Merkels govt, castigated at home for its domestic squabbles and condemned abroad for its handling of the euro crisis raising new questions about whether it can last a full four-year term. Westerwelle has repeatedly rebuffed overtures to work with the SPD in recent years, but he suggested at the weekend that such a link might be possible in NRW. Well have to wait and see which coalition we get in North Rhine-Westphalia, he told newspaper Welt am Sonntag, welcoming the fact that the SPD had decided against a coalition with the Left party in NRW. The NRW talks come against the backdrop of government efforts to agree how to consolidate public finances, already a contentious issue inside the coalition. Merkels cabinet will meet to discuss the planned overhaul on June 6-7. Westerwelles apparent opening to the SPD also follows a plunge in support for his party, whose hopes of cutting taxes were dashed by Merkel a day after the NRW vote. It looks like Westerwelle is annoyed with Merkel, said Gero Neugebauer, a political scientist at Berlins Free University. If the FDP were to enter a coalition with the SPD in NRW, Westerwelle could use it to put pressure on Merkel. This would have an impact on federal policy.