World leaders have gathered in London for a one-day conference aimed at coming up with a coordinated response to decades of instability in Somalia.

British Prime Minister David Cameron said at the outset of the meeting Thursday that he is “absolutely convinced” Somalia can solve its problems and fulfill its potential. While he said the conference is not meant to impose international solutions on Somalia, he said the world will “pay a price” if it fails to help the Horn of African nation recover from violence, famine and poverty.

U.S. Secretary of State Hillary Clinton and U.N. Secretary-General Ban Ki-moon also spoke at the opening of the conference, which is bringing together representatives of 40 countries.

Somalia has endured two decades of civil war and poverty since the fall of its last stable government in 1991. The country's weak Western-backed transitional government has recently struggled to deal with a devastating famine, as well as pirates and Islamist rebels that are seen as a threat to regional security.

Ahead of the conference, Somali Prime Minister Abdiweli Mohamed Ali warned that his country is at a crossroads, and that failure to address its problems would have global ramifications.

“The problems of Somalia – such as piracy, terrorism, anarchy, refugees, famine, droughts – are not unique to Somalia and will not be confined to the borders of Somalia. So we have to all hope to contribute and succeed.”

Somali's government has been involved in a four-year battle with al-Qaida-linked insurgent group al-Shabab, which controls large portions of the country and aims to impose its strict version of Islamic law across the country.

Al-Shabab suffered a major defeat on Wednesday when it was forced to retreat from Baidoa, Somalia's third largest city that has long been considered a rebel stronghold.

Somalia's transitional government also got a boost from the U.N. on Wednesday when the Security Council agreed to expand the African Union Mission in Somalia (AMISOM) by nearly 6,000 troops. Ethiopia, Kenya and the African Union all have contributed soldiers to the fight against al-Shabab.

Thursday's conference will also focus on the establishment of a permanent and representative Somali government before August, when the mandate of the current transitional leadership expires.

The current international plan calls for a new government to be appointed within six months. But critics warn the government may not enjoy much legitimacy unless a new constitution is formed and elections are held in the war-ravaged country.