Chancellor Angela Merkel and her new coalition government have been backed by the Bundestag almost six months after all parties failed to secure a majority in the elections.

With 399 yes votes out of 709, the country's lower house of parliament, the Bundestag on Wednesday approved the alliance made between Merkel's Christian Democratic Union (CDU), its allied Christian Social Union (CSU) and a reluctant partner, the Social Democratic Party (SPD).

The Bundestag also backed Merkel - with 35 fewer supporters than the alliance vote - to be the head of the renewed coalition for four more years that saw her give up six out of 14 cabinet seats to SPD and three more to CSU, being left with only five for her own party.

The alliance has a 177-page coalition agreement signed with detailed objectives set out for each of the four years of cooperation, including 105 pilot projects.

The number one issue that the coalition will tackle in the current year concerns immigration.

With the initiative of Horst Seehofer, the new interior minister, a masterplan will be drawn up for more rapid processing of applications for asylum and more effective deportations.

Top long-term priorities include stabilising pensions after 2025 and attaining the climate targets set for 2020.

This fourth term in office is expected to be the last for Merkel even though German legislation does not limit the number of years a chancellor can serve.

Merkel, who took up the top job in 2005, will become one of the two longest-serving German chancellors by the end of her current term in 2021 with 16 years in charge of Europe's biggest economy.

Helmut Kohl also occupied the chancellor's office for 16 years between 1982 and 1998.

Support for Merkel has declined since she allowed hundreds of thousands of asylum seekers from Syria, Iraq, Afghanistan and other countries into Germany.

The far-right Alternative for Germany (AfD) party used anti-migrant sentiments to draw millions of votes away from Merkel's CDU and other big parties in the September 2017 elections, leaving her without a government majority.