By Andrew Quinn
KAMPALA (Reuters) - U.S. Secretary of State Hillary Clinton said Africa's leaders should respect the rules on Friday when she met Ugandan President Yoweri Museveni, a strong Washington ally who has changed the constitution to prolong his hold on power.
She met Museveni, who is serving his fourth elected term after coming to power in 1986, as part of a seven-nation African tour that began in Senegal on Wednesday.
At their meeting in the capital, Kampala, Clinton urged Museveni, a U.S. security ally whose authoritarian policies have provoked criticism from political opponents and foreign rights groups, to consider his legacy.
She also thanked the veteran leader for helping in Somalia, where Ugandan troops form the backbone of an African Union peacekeeping force battling to restore order to the Horn of Africa nation overrun by al Shabaab Islamist insurgents.
United States Special Forces are also working with Uganda in the hunt for fugitive Lord's Resistance Army (LRA) leader Joseph Kony, across some of Africa's most remote and hostile terrain.
Museveni removed the two-term presidential limit set out in the constitution in 2005, a year before seeking his third term.
His ruling party has shown reluctance to set a new term limit, and this is seen as a sign he is interested in ruling for life, though he himself has said nothing categorical on the issue.
The east African country, which recently discovered commercial oil deposits, is due to hold its next presidential election in 2016 and Museveni is expected to run again.
Although initially lauded for reviving Uganda's economy and "restoring" political stability, Museveni has lately come in for international censure for his increasingly authoritarian rule, for holding on to power, and over corruption in the country.
Clinton urged Museveni to strengthen Uganda's democratic institutions and consider his own legacy.
"Our position is that there has to be a constitution that sets forth the rules that everyone has to follow ... so that it's not about - as President Obama memorably said in Ghana - it's not about strong men, it's about strong institutions," Clinton told reporters in the South Sudan capital, Juba.
U.S. President Barack Obama praised Ghana as a model for democracy and stability when the country's late president John Atta Mills visited Washington earlier this year.
"Each leader will make a different calculation about that, but our relationship is not with individual leaders, over the long run it is with nations, it's with governments, it's with people," Clinton said.
A limit of two five-year presidential terms was added to Uganda's constitution in 1995 to check leaders' inclination to cling to power.
Museveni, however, argued the term limits were an obstacle for a popular leader and in 2005 he persuaded members of his party to scrap the limit. Museveni will only become ineligible to stand when he turns 75, the age limit for a presidential candidate. He is thought to be around 68.
Clinton said good relations between Washington and Kampala were very important to both the United States and Uganda.
"We deeply respect the role that President Museveni has played in his country's history," she said.
(Writing by James Macharia, editing by Tim Pearce)