British train drivers will take three more days of strike action, including coinciding with the soccer FA Cup final on June 3, after rejecting a pay offer from 16 train companies in a long-running dispute, their trade union said on Thursday.

ASLEF said the strikes would take place on May 12, May 31 and June 3. It is also withdrawing non-contractual overtime May 15-20 inclusive, as well as on May 13 and June 1.

As well as the FA Cup final, the action will likely impact those travelling to the Eurovision Song Contest in Liverpool, taking place between May 9 and 13.

"Our executive committee met this morning and rejected a risible proposal we received," Associated Society of Locomotive Engineers and Firemen (ASLEF) general secretary Mick Whelan said in a statement.

"Consequently, we have today announced three more days of strike action."

The Rail Delivery Group (RDG), which represents train operators, said it had offered a pay rise of 8% over two years and described the fresh strike dates as "disappointing".

"More strike action is totally unnecessary and will only heap more pressure on an industry already facing an acute financial crisis," an RDG spokesperson said.

"We urge the ASLEF leadership to re-join us at the negotiating table and work with us to find a solution." (Reporting by Muvija M and Farouq Suleiman, Editing by Kylie MacLellan)