LIMA, Aug 9 (Reuters) - Peruvian central bank President Julio Velarde has agreed to stay on for an extra term, a source familiar with his decision said on Monday, a move poised to calm markets rattled by the election of the country's new left-wing president.

"Julio Velarde has agreed to continue in the role and is following the conversations to define the members of the bank's board," said the source, who declined to be identified because the decision has not yet been made public.

A central bank representative was not immediately available for comment.

Velarde, a prestigious central banker, has been in the role since 2006 and helped cement Peru's economy as one of the most stable in Latin America. Peru's central bank is independent from the government, with the rest of the bank's board split between nominees proposed by the executive and legislative branches.

Newly inaugurated President Pedro Castillo asked Velarde to stay in the role. Velarde initially said he planned to retire later this year.

Peruvian markets have been battered on Castillo's election, with the local sol currency hitting a record low against the dollar on Monday.

Castillo belongs to a Marxist-Leninist party, has named several hardliners to his Cabinet and is pushing to redraft the country's constitution. (Reporting by Marco Aquino; Editing by Christian Schmollinger and Leslie Adler)