What he did cite repeatedly was Iran, along with his vow to prevent Iran not only from "possessing" nuclear weapons, but for speech and actions that call for Israel's destruction.
Abbas and Israeli Prime Minister Benjamin Netanyahu also condemned the Manchester attack.
Rouhani noted the contrast between young Iranians dancing in the streets to mark the re-election of a leader seeking detente with the West, and images of Trump meeting with a galaxy of Arab autocrats, some of whose countries have spawned the Sunni militants hostile to Washington and Tehran alike.
"I think that came across loud and clear", says Rubin. It is not easy, but we agree with him - peace is possible.
United States President Donald Trump said yesterday that Palestinian President Mahmoud Abbas and Israeli Prime Minister Benjamin Netanyahu were prepared to "reach for peace", even as he cautioned that a deal will not be easily achieved.
Police said the attacker detonated the explosives shortly after 10:33 pm (2133 GMT) at Manchester Arena, as thousands of fans streamed out of a concert by USA singer Ariana Grande.
But Trump departed for Europe having offered no real indication of a path forward on one of the world's most intractable disputes. "We must be resolute in condemning such acts in a single, unified voice".
Trump's foreign tour comes in the shadow of difficulties at home, where he is struggling to contain a scandal after firing James Comey as Federal Bureau of Investigation director almost two weeks ago.
In public remarks in the West Bank town of Bethlehem and in Jerusalem, Trump avoided mention of a two-state solution to the Palestinian conflict, and made no references to controversial Jewish settlements or to recognition of Jerusalem as Israel's capital.
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Justin Trudeau had a personal conversation with Trump just hours after his announcement, expressing his own disappointment in the decision.
Instead, he focused on stamping out terrorism.
But while Mr Trump spoke in generalities about the goal, Mr Abbas laid out the specifics of Palestinian demands - which all have been supported by the Arabs and rejected by Israel through decades of unsuccessful peace negotiations shepherded by American presidents.
Trump's comments, the newspaper added, in effect tied "the future of the anti-Iran coalition to the Palestinian issue despite Mr. Netanyahu's longtime efforts to unlink the two".
On Tuesday, another senior USA official said Trump is working on building strong relationships in the Middle East between Israel and its Arab neighbors that will create momentum for a peace deal between Israelis and Palestinians.
The Conference of Presidents of Major American Jewish Organizations praised Trump's condemnation of the PA's continued incitement to terror.
His words matched his actions during his visit here. The area, captured by Israel in 1967, is not sovereign Israeli territory and Palestinians there are not Israeli citizens and do not have the right to vote.
But Trump had no reservations as he placed his note of prayer in between the wall's many cracks and uploaded a photo of his time there as his Twitter cover photo.
Standing with Trump after their talk in Abbas' presidential residence, Abbas said that Palestinians "are committed to working with you to reach a historic peace deal between us and Israel". "It is deeply, deeply appreciated".