NAIROBI (Reuters) - Somalia's political leaders are making encouraging progress toward meeting an August 20 deadline to lay the groundwork for a new constitutional government, U.S. Secretary of State Hillary Clinton said on Saturday.

Clinton met Sheikh Sharif Sheikh Ahmed, president of Somalia's Transitional Federal Government, and other Somali leaders in Nairobi, during a seven-nation African tour.

Somalia has been mired in civil strife, grinding poverty, Islamist militancy and maritime piracy since warlords toppled military dictator Mohamed Siad Barre in 1991, leaving the nation without an effective central government.

An African Union force trying to defeat al Shabaab, an al Qaeda linked Islamist insurgent group that seized control of much of central and southern Somalia, has had some success and driven al Shabaab out of the capital Mogadishu.

But the rebels remain the strongest of an array of militias which have a history of wrecking political settlements and perpetuating war, instability and famine.

"We are very encouraged by the progress the leaders have been making to meet all the requirements of the road map by the Aug 20 deadline," Clinton told reporters.

A U.S.-backed plan calls for Somalia to establish a legitimate government accepted by the country's fractious clans, and a new parliament and constituent assembly to replace institutions plagued by corruption and infighting.

The National Constituent Assembly, sitting in Mogadishu for the last week, approved a provisional constitution to replace an 8-year-old Transitional Federal Charter and lead to the end of the transition process on August 20.

The draft constitution is expected to be put to a nationwide referendum as soon as the security situation improves.

Clinton said she would discuss the remaining tasks ahead, as well as the international support required to strengthen constitutional rule in Somalia.

Her Africa tour is also part of a U.S. push to broaden security partnerships with countries like Uganda and Kenya, which are playing leading roles in helping to stabilize Somalia.

The AU peacekeeping force in Somalia hopes to drive the militants out of the country's central and southern regions this month, when the U.N.-backed government's mandate expires.