France and the US have introduced a draft resolution at the UN Security Council that would allow states to arrest pirates in Somalia's waters.
The document gives nations a six-month mandate to use "all necessary means" to fight piracy.
But it says that countries taking such action should be co-operating with Somalia's embattled interim government.
Piracy is a huge problem off Somalia's coast - there have been more than a dozen attack on ships this year.
In the latest incident, pirates last week seized a Spanish fishing boat with 26 crew members in the region. They later released the hostages for a reported ransom of $1.2m (£600,000).
Earlier this month, six Somalis seized a French luxury yacht with a 30-strong crew. The hostages were later freed, and French commandos detained the attackers.
The draft resolution - which was also co-sponsored by Britain and Panama - expresses deep alarm at the increase in acts of piracy that pose a grave threat "to the safety of commercial maritime routes and to international navigation" off Somalia.
It authorises states to enter the country's territorial waters and "use all necessary means to identify, deter, prevent and repress acts of piracy and armed robbery".
This would include actions such as boarding, searching and also seizing ships engaged in piracy.
"The time has come for the Security Council to respond to the situation," US Ambassador to the UN Zalmay Khalilzad told reporters at the UN headquarters in New York.
"The government of Somalia is not in a position to deal with this problem by itself," he added.
Somalia has not had an effective central government for more than 17 years and is plagued by insecurity.
In February, the Somali government itself asked for the UN Security Council's assistance in tackling piracy in the region.
Diplomats declined to say when the document could be passed, saying there were complex legal issues involved, Reuters reported.
France hopes to expand the same approach to other areas affected by piracy, like the coast of West Africa, the BBC's UN correspondent Laura Trevelyan says.
Meanwhile, Washington wants to keep the focus on Somalia for now, concerned that the Horn of Africa could become a haven for terrorist groups, she adds.