In a statement, Downing Street highlighted a number of joint efforts that were already in place, including a counter-terrorism police unit in Yemen and support for its coastguard operation.
Gordon Brown stressed more was still needed.
"Yemen has been recognised, like Somalia, to be one of the areas where... we've got to do more," he said.
"So it's strengthening counter-terrorism co-operation, it's working harder on the intelligence efforts.
"And of course it's... how we can prevent the perversion of a good religion, Islam, by a group of people who will stop at nothing in a murderous ideology that tries to create a caliphate, tries to create the sense that everybody is an enemy except those people who believe in a particular version of Islam."
The Downing Street statement set out Mr Brown's other intentions:
• Have the evolving threat from Yemen and Somalia placed on the agenda for the EU General Affairs Council in January
• Push for stronger action on Yemen from the Financial Action Task Force, an intergovernmental body set up to combat terrorist financing
• Discuss further the UK's response to the suspected bomb plot at a special meeting of the National Security, International Relations and Development committee (NSID)
Earlier, there was confusion over whether counter-terrorism operations outlined in Downing Street's press statement were new.
It prompted shadow home secretary Chris Grayling to accuse the prime minister of "spin" and playing politics with terrorism.
Following the alleged bomb attack, Yemen said it had the will and ability to deal with al-Qaeda, but needed the West to provide more training, military equipment and transport.
Gen Petraeus, who is responsible for US Middle East and Central Asian operations, has said the US would more than double counter-terror aid to Yemen this year.
During his visit, he met Yemeni President Ali Abdallah Saleh to discuss the militant threat. Yemeni officials said they had sent more troops to fight al-Qaeda militants in the provinces of Abyan, Baida and Shabwa.
On Saturday, US President Obama for the first time publicly accused an offshoot of al-Qaeda, based in Yemen, over the alleged airline plot by Nigerian Umar Farouk Abdulmutallab.
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