He is only the second pope to visit the White House and the first in 29 years to do so.
The statement stressed the two leaders’ desire to see a peaceful Middle East with the creation of an independent Palestinian state living side-by-side at peace with Israel.
They also expressed “their mutual support for the sovereignty and
independence of Lebanon” and denounced terrorism.
“They further touched on the need to confront terrorism with appropriate means that respect the human person and his or her rights,” the statement said.
On the issue of immigration, that has caused conflict between the US and the Vatican, both men said they understood the need “for a coordinated policy regarding immigration, especially their humane treatment and the well being of their families” the statement added.
The pope said in an earlier speech at the White House that the US must do “everything possible to fight … all forms of violence so that immigrants may lead dignified lives”.
He also urged the US to adopt “patient efforts of international diplomacy to resolve conflicts” and promote progress around the world.
Both leaders have previously disagreed over the the war in Iraq and immigration, however they share common ground on opposing abortion, gay marriage and stem cell research.
Hispanics make up nearly 40 per cent of the 70 million Catholics in the US, and are increasingly targeted in efforts to crack down on illegal immigrants.
Al Jazeera’s Rob Reynolds in Washington DC said it seemed that both men were using the visit to put forward their agendas.
On Tuesday, the pope also expressed his shame over sex abuse scandals involving US priests and said he was committed to keeping paedophiles out of the ranks of the clergy.
The trip is the first by a Roman Catholic pope since a wave of abuse scandals began in the US in 2002, provoking legal actions that led to more than $2bn in settlements.
However, he is not expected to meet abused victims of paedophile priests, and one group of victims, the Survivors Network for those Abused by Priests (Snap), said more had to be done.
“We’re way beyond the point at which an apology, a nice gesture, a few soothing words and promises, will be meaningful,” Snap said in a statement quoted by AFP.