At a summit in Uganda, they approved a request to send 2,000 more troops to the Somali capital Mogadishu.
Rules of engagement are to be changed to allow the troops to fire first if they are facing imminent attack.
Ugandan President Yoweri Museveni had wanted a tougher mandate to "eliminate" the al-Qaeda linked group that allowed forces to go on the offensive.
He told the BBC that AU peacekeepers were "confused" by the current mandate.
"They don't understand what they are doing. So they need a robust answer, a robust incisive answer," he said.
Dozens of people were killed two weeks ago in twin bomb attacks in Uganda's capital, Kampala, which al-Shabab said it had carried out.
Mr Museveni's call for the AU force to be able to go on the offensive against al-Shabab was not taken up by the African Union leaders, but the force will now be able to carry out pre-emptive attacks against the hard-line Islamist insurgents.
The summit also approved requests for new equipment for the force.
Troops from Uganda form a large part of the AU's 6,000-strong peacekeeping mission in Somalia. Burundi is the only other country to contribute to the force, known as Amisom.
BBC East Africa correspondent Will Ross says the extra 2,000 troops are likely to come from Guinea and Djibouti - as previously announced - but precise numbers and dates for their deployment remain unclear.
Before the Kampala summit, Somalia's embattled UN-backed government had asked for troops from Muslim countries to prevent al-Shabab portraying the AU force as "infidels".
Both Guinea and Djibouti have Muslim majorities.
The government, backed by the AU, controls only a few parts of the capital, Mogadishu, while al-Shabab and its allies run much of southern Somalia.
The African leaders gathered in Kampala amid tight security and a heavy military presence.
They observed a two-minute silence for the victims of the 11 July bomb attacks, which targeted people who were watching the football World Cup final at a Kampala restaurant and a sports ground.
Mr Museveni told AU delegates that "many of the organisers" of the attack had been arrested and their interrogation was "yielding very good information".
In a statement released before the meeting, Mr Museveni said the attacks would worsen al-Shabab's situation.
"These reactionary groups have now committed aggression against our country," the statement said. "We have a right of self-defence. We shall now go for them."
Our correspondent says there is concern that any offensive against al-Shabab could increase the number of civilian deaths and make the AU mission extremely unpopular with the Somali population.__________________________________________________________________________________
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