"We will continue to act very aggressively against Iran's efforts to entrench in Syria," he said in a statement. "We do not intend to reduce our efforts. We will intensify them, and I know that we do so with the full support and backing of the United States."
The US announced Wednesday that it would begin withdrawing its some 2,000 troops from Syria at once, with Donald Trump claiming victory over Islamic State and declaring that there was no longer any reason to keep American forces there.
The decision drew widespread criticism, with many analysts saying this was a win for Russian President Vladimir Putin, whose country becomes the main military power in Syria, and warning that IS still has tens of thousands of fighters in the country.
Putin welcomed the US decision on Thursday, telling reporters at his annual news conference that he agreed with Trump's assessment that the defeat of the Islamic State group removes the need for the US military presence.
Putin reaffirmed the long-held Russian argument that the US presence in Syria is illegitimate because it hadn't been vetted by the UN Security Council or approved by Syrian President Bashar Assad's government. Putin added that "if the US decided to withdraw its contingent, it has done the right thing."
Russia is a key ally of Assad, and its military intervention beginning in 2015 turned the tide of the war in his favor.
The Russian leader says it remains to be seen if the US carries out its intention, noting Washington's repeated promises to end its 17-year presence in Afghanistan.
A US-backed Kurdish group in Syria on Thursday rejected Trump's claim that IS has been defeated, saying the withdrawal of US troops would lead to a resurgence of the extremist organization.
The Syrian Democratic Forces said in a statement that a premature US troop pullout would have dangerous repercussions and a destabilizing effect on the region.
"The war against Islamic State has not ended and the group has not been defeated," said the group, in its first response to Trump's surprise announcement Wednesday.
Trump's decision to withdraw troops from Syria has rattled Washington's Kurdish allies, who are its most reliable partner in Syria and among the most effective ground forces battling IS. With US air support, the Kurds drove IS from much of northern and eastern Syria in a costly four-year campaign.
Kurdish officials and commanders met into the night, discussing their responses to the decision, local residents said Thursday.
Arin Sheikmos, a Kurdish journalist and commentator, said "we have every right to be afraid."
"If the Americans pull out and leave us to the Turks or the (Syrian) regime our destiny will be like the Kurds of Iraqi Kurdistan in 1991 -- million of refugees, there will be massacres. Neither the regime, not Iran nor Turkey, will accept our presence here," he said.
Trump's decision to withdraw is widely seen as an abandonment of a loyal ally. Turkish President Recep Tayyip Erdogan has repeatedly threatened to launch a new offensive against the Kurds. The threat from Turkey could drive the Kurds into the arms of Syrian President Bashar Assad, and by extension Iran and Russia.
Turkey views the People's Protection units, or YPG, the main component of the Syrian Democratic Forces, as a terrorist group and an extension of the insurgency within its borders. US support for the group has strained ties between the two NATO allies.
"This is expected," Ebrahim Ebrahim, a Syrian Kurd based in Europe, said of the pullout. "But it is not just treason to the Kurds or the people of Syria but to democracy, to morals, if this is true. Yes, true, we fought for ourselves, but we also fought for democracies all over the world," he added.
A Syrian member of parliament, Peter Marjana, said Thursday that a US pullout would be a "recognition that Syria has won."
Trump's contention that IS has been defeated contradicted his own experts' assessments and shocked his party's lawmakers, who called his decision rash and dangerous.
The US began airstrikes against IS in Syria in 2014, and later sent in ground troops to aid Kurdish forces. Trump abruptly declared their mission accomplished in a tweet.