Francis and Erdogan last met in 2014 during the pope's visit to Turkey.
Both the Turkish and Vatican sides described the private talks as cordial.
They declared Trump's decision "null and void legally" and "a deliberate undermining of all peace efforts" that would give impetus to "extremism and terrorism".
After the meeting, the Pope gave Mr Erdogan a bronze medallion showing an angel embracing the world while battling a dragon.
Day, Noren need another day to decide victor at Torrey
Noren found the water with his second shot of the morning while Day placed his third inches from the cup to seal their fates. Palmer was eliminated on the first playoff hole, but four more holes after that was not enough to separate Day and Noren.
Pope Francis and later the European Union in 2015, the massacre's centennial, were trying to encourage Turkey "to recognize the Armenian genocide and thus pave the way for a genuine reconciliation between Turkish and Armenian peoples".
A Vatican statement issued following the meeting said discussions focussed on the "situation in the Middle East, with particular reference to the status of Jerusalem highlighting the need to promote peace and stability in the region through dialogue and negotiation, with respect for human rights and global law".
Police earlier said around 150 people took part in the authorised demonstration, organised by Italy's Kurdistan Network, in the gardens of Castel Sant'Angelo, outside the "green zone" cordoned off by police in central Rome. Several also held signs calling for the release of Abdullah Öcalan, a Kurdish nationalist leader who has been jailed in Turkey since 1999. A protester was hurt and two were arrested. At least one demonstrator was injured, a witness told Reuters.
"In Afrin, a new crime against humanity is underway", said a Kurdish association based in Italy.
Chiefs agree to trade QB Smith to Redskins
Not only will Cousins set the quarterback market, his decision will have a trickle-down effect around the league. He has been the Chiefs' starting quarterback the last five seasons, including four playoff appearances.
Mostly rain in store for Super Bowl Sunday
Breezy, with a south wind 11 to 18 miles per hour , with gusts as high as 24 miles per hour . Tonight there is a 30 percent chance of scattered snow showers mainly before 9 p.m.
North and South Korea's ice hockey team lose in debut
Moon is known to be hoping that the US and North Korea could hold talks in the South when their high-ranking officials visit here. Twenty-two North Korean athletes will compete in the Olympics , including 12 who will play in a unified women's ice hockey team.
Polar bears go hungry as the Arctic ice melts
Even though the findings are based on only a few female polar bears, the result will be same for the polar bears of other areas. While four bears put on weight, five bears lost up to 10 per cent of their body weight - between 18 and 20 kg - in 10 days.
At least 17 killed, 110 wounded in Afghan auto bomb attack
Thick, dark smoke can be seen rising into the sky following a loud explosion near the old Interior Ministry building Saturday. Wounded people are assisted at the site of an explosion in downtown Kabul, Afghanistan , Saturday, Jan. 27, 2018.