* EU leaders to launch push for tighter bank rules

* Barroso to get political backing for new Commission term

* Ireland hopes for guarantees on Lisbon treaty

By Mark John

BRUSSELS, June 18 (Reuters) - European Union leaders will approve new rules to tighten bank supervision at a two-day summit which starts on Thursday and is intended to show the bloc has the economic crisis under control.

The leaders will support conservative Jose Manuel Barroso's bid for a second five-year term as president of the European Commission, providing some continuity in difficult times.

They are also due to agree legal guarantees to help persuade Irish voters to back the Lisbon treaty reforming decision making in the EU after its expansion to 27 member states.

The summit follows an election to the European Parliament in which there was a record-low turnout, attributed partly to disenchantment with the Union's patchy response to a crisis that has cost jobs and caused street protests across the region.