"President Abbas outlined his plans for a new, technocratic Palestinian government, committed to the Quartet principles, including non-violence and the recognition of Israel," Xinhua quoted a Downing Street spokesperson as saying in a statement after the meeting.
Abbas also expressed his readiness to resume peace talks with Israel and his hope that this could be achieved rapidly.
Cameron urged progress towards securing the rapid resumption of peace talks, which remain "the only viable route to a lasting solution".
"The Prime Minister reiterated our support for a two-state solution and the UK's support to the Palestinian Authority," the spokesperson added.
Cameron also expressed his desire to build on the economic progress in the Palestinian territories, particularly in the West Bank.
A meeting between Abbas and US Secretary of State John Kerry is also scheduled Thursday in London to evaluate the course of the Palestinian-Israeli peace process, according to Palestinian Minister of Foreign Affairs Riad al-Maleki.
Abbas and Kerry are expected to talk about the reasons that led to the failure of the peace talks and discuss the possibility of resuming peace negotiations.
Israel suspended the US-mediated peace negotiations with the Palestinians five days before they officially ended in response to the reconciliation agreement signed April 23 between Abbas's Fatah party and Hamas rulers of Gaza.
Following the signing of the reconciliation deal, Israeli Prime Minister Benjamin Netanyahu said Israel will not negotiate with any Palestinian government unless it recognises the state of Israel.