The issue of whether the president of the United States should sit down to talk with the leaders of terrorist groups or terrorist supporting states is one requiring some thought to perceive a direction to take supported by Catholic teaching.
The ancient dictum that talking about problems is better than fighting about them can certainly guide us, as well as the more modern perception of the legitimacy a leader gives an opposing leader resulting from an open-ended meeting.
In the Catechism of the Catholic Church, the section on Safeguarding Peace, under the precepts for observing the Fifth Commandment “You shall not kill.” is guidance.
III. Safeguarding Peace
Peace
2302 By recalling the commandment, "You shall not kill,"93 our Lord asked for peace of heart and denounced murderous anger and hatred as immoral.
Anger is a desire for revenge. "To desire vengeance in order to do evil to someone who should be punished is illicit," but it is praiseworthy to impose restitution "to correct vices and maintain justice."94 If anger reaches the point of a deliberate desire to kill or seriously wound a neighbor, it is gravely against charity; it is a mortal sin. the Lord says, "Everyone who is angry with his brother shall be liable to judgment."
2303 Deliberate hatred is contrary to charity. Hatred of the neighbor is a sin when one deliberately wishes him evil. Hatred of the neighbor is a grave sin when one deliberately desires him grave harm. "But I say to you, Love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven."
2304 Respect for and development of human life require peace. Peace is not merely the absence of war, and it is not limited to maintaining a balance of powers between adversaries. Peace cannot be attained on earth without safeguarding the goods of persons, free communication among men, respect for the dignity of persons and peoples, and the assiduous practice of fraternity. Peace is "the tranquillity of order." Peace is the work of justice and the effect of charity.
2305 Earthly peace is the image and fruit of the peace of Christ, the messianic "Prince of Peace." By the blood of his Cross, "in his own person he killed the hostility," he reconciled men with God and made his Church the sacrament of the unity of the human race and of its union with God. "He is our peace." He has declared: "Blessed are the peacemakers."
2306 Those who renounce violence and bloodshed and, in order to safeguard human rights, make use of those means of defense available to the weakest, bear witness to evangelical charity, provided they do so without harming the rights and obligations of other men and societies. They bear legitimate witness to the gravity of the physical and moral risks of recourse to violence, with all its destruction and death.