Some nations are seeking exemptions on certain types of cluster weapons.
Areas of negotiation at the summit include more time for some countries to dismantle their arsenals and transition periods in which they could still be used.
Campaigners oppose any watering down of an agreement and hope a ban would stigmatise the use of cluster munitions by non-signatories.
Mark Garlasco, a campaigner for New-York based Human Rights Watch spoke to Al Jazeera from Dublin.
Garlasco said: “I have seen cluster munitions used across the world… in Lebanon… in Iraq. These are the types of weapons that should never be used. There is no way to use these weapons in a legal manner.
“The vast majority of the world is clearly here in support of the treaty. At the end of the two weeks we are certainly going to have a treaty, the question then becomes what form it will take?
“Will it be the strong treaty that we have now for a total ban or will it be watered down by some of the other nations that are surrogates to the United States?”
On Sunday, Pope Benedict XVI called for an international treaty that would be both strong and credible.
The conference was opened by Michael Martin, Ireland’s foreign minister, whose government has previously said it would campaign for a complete ban.
However, Martin said that if that was not possible they would seek agreement on an “immediate freeze” on their use.
The negotiations on banning cluster bombs, which were started by Norway in February 2007, have taken the same path as the landmark 1997 Ottawa Treaty ban on anti-personnel landmines.
Both processes have gone outside the United Nations to avoid vetoes and attempt to agree a treaty more quickly.
Cluster munitions caused more civilian casualties in Kosovo in 1999 and Iraq in 2003 than any other weapon system.
Israel used cluster bombs widely during the 2006 war in Lebanon and many were left behind following a ceasefire between the two countries.
The Cluster Munition Coalition, a network of around 200 civil society organisations aiming at banning the weapons, has said that there were more than 200 civilian casualties in Lebanon in the year after the ceasefire as a result of cluster bombs.