WASHINGTON (Reuters) - Treasury Secretary Timothy Geithner said on Tuesday that future mortgage costs likely will be "modestly higher" after reforms are completed to the national housing finance system.

Testifying before the House Financial Services Committee, Geithner said it will take some years to complete an overhaul of the system and to wind down Fannie Mae and Freddie Mac but said it was important for lawmakers to begin the effort.

Geithner said housing markets were "still in a very difficult state" and cautioned that the administration and lawmakers must be careful not to jeopardize a broader economic recovery while dealing with housing finance reform.

(Reporting by Glenn Somerville, Editing by W Simon )