During a march in Beirut, protesters chanted “Death to America, death to Israel.”
The Russian president said Moscow’s naval and air bases in Syria would keep operating.
Trump’s decision last week to recognize Jerusalem as the Israeli capital has set off rage in the region.
The announcement by the Iraqi prime minister came almost in passing, reflecting a nationwide fatigue with the bloody three-year fight.
In Jerusalem and the wider region, demonstrations appeared less intense.
The Hamas militant group urged followers to mount a third intifada, or uprising, against Israel.
In the Middle East, even staunch ally Saudi Arabia called the decision “irresponsible.” Iraq called it “unjust.”
On a rainy day that curbed public demonstrations, Palestinians predicted another intifada and Israelis voiced gratitude.
What amounted to an unusually harsh rebuke came as the Saudi-led coalition intensified airstrikes.
Analysts say the move could threaten Israel’s improving relations with Sunni Arab countries.
The secretary of state said at NATO headquarters that President Trump remains “very committed to the Middle East peace process.”
Several countries warned that the move could also disrupt hopes for a Mideast peace deal.
Both countries are girding for a wave of terrorist attacks as ISIS returns to its insurgent roots and political rivalries remain unresolved.
Jordan and Egypt join the backlash, claiming such a decision could collapse peace efforts and ignite unrest.
Reports indicated he was killed by the rebel group known as the Houthis, former allies he had split with last week.